Answer:
True, see proof below.
Step-by-step explanation:
Remember two theorems about continuity:
If f is differentiable at the point p, then f is continuous at p. This also applies to intervals instead of points.(Bolzano) If f is continuous in an interval [a,b] and there exists x,y∈[a,b] such that f(x)<0<f(y), then there exists some c∈[a,b] such that f(c)=0.If f is differentiable in [0,4], then f is continuous in [0,4] (by 1). Now, f(0)=-1<0 and f(4)=3>0. Thus, we have the inequality f(0)<0<f(4). By Bolzano's theorem, there exists some c∈[0,4] such that f(c)=0.
The question is about the intermediate value theorem in calculus, which states a function takes on every value between f(a) and f(b) in a closed interval [a, b]. Given the function's values at 0 and 4, it must cross the x-axis, or equal zero, somewhere in the interval [0, 4].
Explanation:This is a question about intermediate value theorem, a fundamental theorem in calculus. The intermediate value theorem states that if a function is continuous on a closed interval [a, b], then it takes on every value between f(a) and f(b) at some point within that interval. If we know that f(0) = -1 and f(4) = 3, this means the function f crosses the x-axis (or, in other words, f(c) = 0 for some c) somewhere in the interval [0, 4] because zero lies between -1 and 3 (the function's values at 0 and 4 respectively).
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A figura a seguir representa a planta de um apartamento . O dono desse apartamento deseja colocar carpete na sala e no dormitório .Sabendo que o metro quadrado colocado do carpete escolhido custa 48reais quanto o dono do apartamento deverá gastar?
Answer:
O dono deverá gastar 1764 reais
Step-by-step explanation:
Oi!
Em anexo, você encontrará a figura do apartamento que encontrei na web.
Para encontrar a superfície do tapete que o proprietário precisa comprar, precisamos encontrar a superfície do dormitório e da sala.
Superfície do dormitório:
A superfície do dormitório é calculada multiplicando a base pela altura do retângulo.
Da figura:
base = 3,5 m
altura = 3 m
Superfície do tapete do dormitório = 3,5 m · 3 m = 10,5 m²
A superfície da sala de estar é a superfície do retângulo composto pela sala e pelo banheiro menos a superfície do banheiro:
superfície da sala de estar = superfície do retângulo sala / banheiro - superfície do banheiro
Superfície do banheiro:
Conhecemos um lado do banheiro: 2 m
O outro lado será:
lado do banheiro = 9 m - 3,5 m - 3,5 m = 2 m
Então, a superfície do banheiro será:
Superfície do banheiro = 2 m · 2 m = 4 m²
Superfície da sala / banheiro
A altura do retângulo é (3 m + 2,5 m) 5,5 m
A base do retângulo é (9 m - 3,5 m) 5,5 m
Então, a superfície da sala / banheiro é (5,5 m) ² = 30,25 m²
Superfície da sala
A superfície da sala será igual à superfície da sala / banheiro menos a superfície do banheiro:
Superficie da sala = 30,25 m² - 4 m² = 26,25 m²
A superfície do tapete será (26,25 m² + 10,5 m²) 36,75 m²
Como cada metro quadrado custa $ 48, o proprietário terá que gastar
(48 reais / m² · 36,75 m²) 1764 reais.
Tenha um bom dia!
Ali simplifies the expression 9y+y to 9y2. Use the drop-down menus to complete the statements below to explain why Ali's solution is correct or incorrect.
Answer:
ali's solution is incorrect
9y+y is the same as 9y+1y
9y^2 is the same as 9y x y
9y+y simplifies to 10y.
Step-by-step explanation:
Answer:
The Middle One which says 9Y2 is the same as 9y . 2y
Step-by-step explanation:
Susan wanted to know if aerobic exercise caused more weight loss than just walking. Susan had her experimental group do aerobic exercise for 20 minutes, 4 days a week. She weighed each subject before the experiment started and again 3 months into the experiment. The independent variable in her experimental research was _____
Answer:
Independent variable : Anaerobic Exercise
Step-by-step explanation:
The dependent variable is known as the variable of interest or "Y" and usually the independent variables are expressed by "X".
The independent variable is the "variable that is changed or controlled in a scientific experiment to test the effects on the dependent variable"
For this case our independent variable would be the anerobic exercise, since we want to se the effect of the exercise on the weigth loss, so then our dependent variable would be th weigth loss.
And for this case we can check the hypothesis with a paired t-test if we use the same individuals.
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations we can use it.
The independent variable in Susan's experimental research on weight loss is the introduction of aerobic exercise. How much weight loss is achieved can have multiple contributing factors, including individual differences. Incorporating moderate to vigorous physical activity is crucial for weight control and may need to be adjusted based on individual needs.
The independent variable in Susan's experimental research is the type of exercise performed by the subjects — specifically, the aerobic exercise. This is because the independent variable is the factor that the researcher manipulates to determine if it causes a change in another variable. In this case, the independent variable is the introduction of aerobic exercise compared to just walking. Susan's goal is to measure the effects of aerobic exercise on weight loss among the participants over a period of 3 months.
Variations in weight loss outcomes in a workout program can be attributed to individual differences such as metabolism, diet, genetics, lifestyle, and adherence to the exercise regimen. For effective weight control, research suggests a combination of aerobic activity and muscle-strengthening exercises. Susan can compare her findings to these variables to gain insight into the weight loss effects of aerobic exercise.
For those looking to use physical activity for weight loss and control, it might make sense to increase either the intensity or the minutes per week of physical activity, depending on their individual circumstances. Incorporating moderate to vigorous aerobic activity combined with a reduction in caloric intake can help meet weight-control goals for many adults.
Three consecutive odd integers have a sum of 27. What is the greatest of these integers?
Answer:
11
Step-by-step explanation:
The middle of the three is their average, their sum divided by 3:
middle = 27/3 = 9
Then the largest is 2 more. It is 11.
Suppose the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs." That is, if P = profit, then P X 0.75 0.05. Use a linear transformation of your results in (a) and (b) to find the mean and standard deviation for P.
Answer:
Step-by-step explanation:
Given that the profit the company makes on each customer visit is $0.75 per DVD minus $0.05 "fixed costs."
i.e. Profit
= P(x) = 0.75 x - 0.05 where x is the no of dvds sold
E(x) = [tex]E(0.75x-0.05)\\= E(0.75x) -E(0.05)\\= 0.75E(x) -0.05[/tex]
(using linear transformation rules for mean)
VarP(x) = [tex]Var(0.75 x - 0.05)\\= Var(0.75x)\\= 0.75^2 Var(x)[/tex]
Hence std dev P(X) = 0.75 std dev (x)
Which statements are true about reflections? Check all that apply.
An image created by a reflection will always be congruent to its pre-image.
An image and its pre-image are always the same distance from the line of reflection
If a point on the pre-image lies on the line of reflection, the image of that point is the same as the pre-image.
The line of reflection is perpendicular to the line segments connecting corresponding vertices.
The line segments connecting corresponding vertices are all congruent to each other.
The line segments connecting corresponding vertices are all parallel to each other.
Answer:1 2 34 6
Step-by-step explanation:
Just answered it
Answer:
1,2,3,4,6
Step-by-step explanation:
Edge 2021
A café owner wanted to compare how much revenue he gained from lattes across different months of the year. What type of variable is ‘month’?
Final answer:
The 'month' variable referenced by the café owner is a categorical variable used to group revenue data across different time periods within a year.
Explanation:
In the context of the café owner's situation, the type of variable that 'month' represents is a categorical variable. A categorical variable is one that has two or more category values and can be used to group or label individuals or items in a dataset. In this case, 'month' is used as a means to categorize the revenue data collected over different time periods within a year, allowing the café owner to compare the performance of latte sales across these distinct categories.
John sells tickets to a school concert. Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales and he sells twice as many adult tickets as children's tickets. How many tickets does he sell all together?
Answer: The total number of tickets that John sold is 27
Step-by-step explanation:
Let x represent the number of adult tickets that John sold at the concert.
Let y represent the number of children's tickets that John sold at the concert.
Adult tickets cost $6.50 and children's tickets cost $4.50. John collects a total of 157.50 from the ticket sales it means that
6.5x + 4.5y = 157.5 - - - - - - - - - -1
John sells twice as many adult tickets as children's tickets. This means that
x = 2y
Substituting x = 2y into equation 1, it becomes
6.5 × 2y + 4.5y = 157.5
13y + 4.5x = 157.5
17.5y = 157.5
y = 157.5/17.5 = 9
x = 2×9 = 18
The total number of tickets that John sold is 9 + 18 = 27
How many positive multiples of 7 that are less than 1000 end with the digit 3?
Answer:
14
Step-by-step explanation:
Ordinarily, a quick multiplication of 7 by other integers up to 10 indicates that only 7*9 yields 63, i.e ends with 3 as required.
Thus the set of possible multiples of the integer 7 ending with the digit 3 will form the arithmetic series with the first term being Ao = 63 and the common difference being d= 7*10= 70. That is we can see the series in details....
the nth term could be evaluated from the formular
An=Ao+(n-1)d (1)
The series could be explicitly depicted as follows:
9*7=63= 63+70*0
(10+9)*7=133 = 63+70*1
(20+9)*7=203=63+70*2
(30+9)*7=273=63+70*3
.................................
(130+9)*7=973=63+70*13
The last 'n' corresponding to the problem statement could be evaluated from equation (1), assuming An=1000:
1000=63+(n-1)*70
1000-63=70(n-1)
937/70=13.38=n-1
n=14.38
Thus the number of possible multiples of 7 less than 1000 ending with digit 3 will be 14.
Check: 7 times 142 is 994, so there are exactly 142 positive multiples of 7 less than 1000.
One tenth of these, ignoring the decimal fraction, end with a digit of 3.
A researcher computes the definitional formula for SS, and finds that Σ(x − M) = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the computational formula?
A. 3.7
B. 4.0
C. 44
D. not possible to know because the scores are not given
Answer:
Option B.
Step-by-step explanation:
Given information:
Σ(x − M) = 44
where, M is mean.
Sample size = 12
The computational formula for sample variance is
[tex]s^2=\dfrac{\sum (x-M)^2}{N-1}[/tex]
where, M is sample mean and N is sample size.
Substitute Σ(x − M) = 44 and N=12 in the above formula.
[tex]s^2=\dfrac{44}{12-1}[/tex]
[tex]s^2=\dfrac{44}{11}[/tex]
[tex]s^2=4.0[/tex]
The sample variance is 4.0.
Therefore, the correct option is B.
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down. Which rule describes the
translation?
(x, y) - (x + 3, y - 4)
(x, y) - (x +3, y + 4)
(x, y) - (x + 4, y-3)
(x, y) - (x + 4, y + 3)
Answer:
[tex](x,y) - (x + 4, y-3)[/tex]
Step-by-step explanation:
Given:
A triangle is drawn on the coordinate plane. It is translated 4 units right and 3 units down.
It is translated 4 units right and 3 units down.
We need to find the rule of translation.
Solution:
Now to the right of the axis which is positive of X axis and 4 units to the right means 4 units are added to X co-ordinate.
Also to the Down of the axis which is negative of Y axis and 3 units to the down means 3 units are Subtracted to Y co-ordinate.
Hence The co-ordinates at which triangle is drawn is [tex](x + 4, y-3)[/tex]
At a summer camp there is one counselor for every 6 campers. Write a direct variation equation for the number of campers, y, that there are for x counselors. Then graph.
Answer:
The direct variation equation can be given as:
[tex]y=6x[/tex]
Step-by-step explanation:
Given:
At a summer camp there are 6 campers under one counselor.
To find the direct variation equation for the number of campers in terms of number of counselor.
Solution:
[tex]y\rightarrow[/tex] Number of campers
[tex]x\rightarrow[/tex] Number of counselors
We have [tex]y[/tex] ∝ [tex]x[/tex]
The direct variation equation can be written as:
[tex]y=kx[/tex]
where [tex]k[/tex] is the direct variation constant.
There are 6 campers under one counselor. Using this statement we can find value of [tex]k[/tex]
Given: when [tex]x=1[/tex] then [tex]y=6[/tex]
We have,
[tex]6=k(1)[/tex]
∴ [tex]k=6[/tex]
Thus, the direct variation equation can be given as:
[tex]y=6x[/tex]
We can find the points using the equation to plot.
[tex]x[/tex] [tex]y=6x[/tex]
0 0
1 6
2 12
The graph is sown below.
A solid object may be drawn as a flat plane object showing all sides, or it may be drawn as an isometric drawing. From the list below, choose which statements about solid objects drawn as isometric drawings are true. I. Circles are drawn exactly as circles. II. Circles are drawn as ellipses and not as exact circles. III. Horizontal lines are drawn at 30° angles above the horizontal. IV. Horizontal lines are drawn at 60° angles above the horizontal. V. Vertical lines are drawn at 90° angles above the horizontal. VI. Vertical lines are drawn at 120° angles above the horizontal.
Answer:
For isometric drawings, these are true :
II. Circles are drawn as ellipses and not as exact circles.
III. Horizontal lines are drawn at 30° angles above the horizontal.
V. Vertical lines are drawn at 90° angles above the horizontal.
Step-by-step explanation:
Now,
An isometric drawing allows the designer to draw an object in three dimensions. Isometric drawings are also called isometric projections. This type of drawing is often used by engineers and illustrators that specialize in technical drawings.
For example, when an engineer has an idea for a new product, he or she will probably create a sketch to show a client or investor. And chances are, the sketch will be an isometric drawing.
In isometric projections, horizontal lines are drawn at 30° to the original horizontal, where as vertical lines are remained unchanged.
Even though horizontal lines are at 30°. the measurements of length does not change. so, the circle look like an ellipse.
⇒ The true statements are:
II. Circles are drawn as ellipses and not as exact circles.
III. Horizontal lines are drawn at 30° angles above the horizontal.
V. Vertical lines are drawn at 90° angles above the horizontal.
In an isometric drawing, circles are represented as ellipses (II), the horizontal lines are commonly drawn at 30° angles above the horizontal (III), and the vertical lines are drawn at 90° angles above the horizontal (V).
Explanation:From the given list, statements II, III, and V about isometric drawings of solid objects are true. II. In isometric drawings, circles are not drawn as exact circles but are instead represented as ellipses. This is due to the three-dimensional perspective presented in isometric drawings making the circle appear distorted. III. Horizontal lines in isometric drawings are commonly drawn at 30° angles above the horizontal line that forms part of the axonometric grid. This provides a consistent upward inclination for all lines sketched or perceived as horizontal in the actual object. V. Vertical lines are drawn at 90° angles above the horizontal. In isometric projections, just like in any form, the vertical lines always maintain the same 90° angle with respect to ground regardless of the viewpoint.
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Solve for x.
3x - 1/5 = 10
A) 1
B) 17
C) 3
D) 6
Answer:
The answer to your question is None of the answers is correct
Step-by-step explanation:
[tex]3x - \frac{1}{5} = 10[/tex]
Solve for x
[tex]3x = 10 + \frac{1}{5}[/tex]
[tex]3x = \frac{50 + 1}{5}[/tex]
[tex]3x = \frac{51}{5}[/tex]
[tex][tex]x = \frac{17}{5} [/tex]x = \frac{51}{(3)(5)}[/tex]
[tex]x = \frac{17}{5}[/tex]
A consumer claims that the mean lifetime of a brand of fluorescent bulbs is less than1500 hours. She selects 25 bulbs and finds the mean lifetime to be 1480 hours with the standard deviation of 80 hours. If you were to test the consumer's claimat the 0.05 significance level, what would you conclude?
Answer:
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1500 hours
Sample mean, [tex]\bar{x}[/tex] = 1480 hours
Sample size, n = 25
Alpha, α = 0.05
Sample standard deviation, s = 80 hours
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1500\text{ hours}\\H_A: \mu < 1500\text{ hours}[/tex]
We use one-tailed(left) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{1480-1500}{\frac{80}{\sqrt{25}}}= -1.25[/tex]
Now,
[tex]t_{critical} \text{ at 0.05 level of significance, 24 degree of freedom } = -1.71[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to reject the null hypothesis and accept the null hypothesis.
We conclude that the mean lifetime of a brand of fluorescent bulbs is equal to 1500 hours.
After performing a one-sample t-test, the calculated t value of -1.25 does not exceed the critical value of -1.711 at the 0.05 significance level. Therefore, we do not have sufficient evidence to support the claim that the mean lifetime of the bulbs is less than 1500 hours.
Explanation:The question asks to test the claim that the mean lifetime of a certain brand of fluorescent bulbs is less than 1500 hours. To test this at the 0.05 significance level, we would perform a one-sample t-test since the sample size is less than 30, and we do not know the population standard deviation.
First, we formulate our null hypothesis (H0) as the mean lifetime of the bulbs being 1500 hours or more, and the alternative hypothesis (Ha) being the mean lifetime less than 1500 hours.
Next, we calculate the test statistic using the sample mean, population mean, standard deviation, and sample size:
[tex]t = (Sample Mean - Population Mean) / (Standard Deviation / \sqrt(Sample Size))[/tex]
[tex]= (1480 - 1500) / (80 / \sqrt(25))[/tex]
= -20 / (80 / 5)
= -20 / 16
= -1.25
Then, we check this t value against the t-distribution table for 24 degrees of freedom (df = n - 1) at the 0.05 significance level. The critical value for a one-tailed test with df = 24 at alpha = 0.05 is approximately -1.711. Since our calculated t value of -1.25 is not less than -1.711, we do not reject the null hypothesis.
Conclusion: At the 0.05 significance level, we do not have sufficient evidence to support the consumer's claim that the mean lifetime of the bulbs is less than 1500 hours.
At the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red?
Answer:
25%.
Step-by-step explanation:
We have been given that at the end of the day, February 14th, a florist had 120 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed.
We are also told that 1/3 of the roses were short-stemmed.
[tex]\text{Short-stemmed roses}=120\times \frac{1}{3}=40[/tex]
Since 20 of those were white and 15 of which were pink, so short stemmed red roses would be [tex]40-(20+15)=40-35=5[/tex].
Now, we will find number of long-stemmed roses by subtracting number of short-stemmed roses from total roses as:
[tex]\text{Long-stemmed roses}=120-40=80[/tex]
We are also told that none of the long-stemmed roses were white, so total number of white roses would be [tex]20+0=20[/tex].
Let p represent the number of total pink roses.
Now, total number of red roses would be total roses (120) minus total pink roses (p) minus total white roses (20).
[tex]\text{Total red roses}=120-p-20[/tex]
[tex]\text{Total red roses}=100-p[/tex]
We have been given that the percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. We can represent this information in an equation as:
[tex]\frac{\text{Short-stemmed pink roses}}{\text{Total pink roses}}=\frac{\text{Short-stemmed red roses}}{\text{Total red roses}}[/tex]
[tex]\frac{15}{p}=\frac{5}{100-p}[/tex]
Let us solve for p by cross-multiplication:
[tex]1500-15p=5p[/tex]
[tex]1500-15p+15p=5p+15p[/tex]
[tex]1500=20p[/tex]
[tex]20p=1500[/tex]
[tex]\frac{20p}{20}=\frac{1500}{20}[/tex]
[tex]p=75[/tex]
Since total number of pink roses is 75, so total number of red roses would be [tex]100-75=25[/tex].
We already figured it out that 5 roses are short-stemmed, so long-stemmed roses would be [tex]25-5=20[/tex].
Now, we have long stemmed roses is equal to 20 and total long-stemmed roses is equal to 80.
Let us find 20 is what percent of 80.
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{20}{80}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=\frac{1}{4}\times 100[/tex]
[tex]\text{Percentage of the long-stemmed roses that were red}=25[/tex]
Therefore, 25% of the long-stemmed roses were red.
In the election for presidency, Stan Fitz received 542 votes, Elizabeth Stuckey received 430 votes and Gene Sterner received 130 votes. Ninety percent of those eligible to vote did so. What was the number of eligible voters?
Answer:
The total number of eligible voters in the town = 1224 ( app.)
Step-by-step explanation:
Let us assume the total number of eligible voters = p
Now, the number of votes received by Stan Fitz = 542
The number of votes received by Elizabeth Stuckey = 430
The number of votes received by Gene Sterner = 130
So, the total number of votes received in total = 542 + 430 + 130 = 1,102
Now, only the 90% of total voters p voted in the election.
⇒ 90% of p = 1102
[tex]\implies \frac{90}{100} \times p = 1102\\ \implies p = \frac{1102\times 100}{90} = 1224[/tex]
or, p ≈ 1224
Hence, the total number of eligible voters in the town = 1224 ( app.)
A rectangular area is to be enclosed by a wall on one side and fencing on the other three sides. If 18 meters of fencing is are used, what is the maximum area that can be enclosed?
A: 9/2 m^2
B:81/4 m^2
C: 27 m^2
D: 40 m ^2
E: 81/2 m^2
Explanation:
Let L be the length and W be the width.
We have only 2 sides are fenced
Fencing = 2L + W
Fencing = 18 m
2L + W = 18
W = 18 - 2L
We need to find what is the largest area that can be enclosed.
Area = Length x Width
A = LW
A = L x (18-2L) = 18 L - 2L²
For maximum area differential is zero
So we have
dA = 0
18 - 4 L = 0
L = 4.5 m
W = 18 - 2 x 4.5 = 9 m
Area = 9 x 4.5 = 40.5 m² = 81/2 m²
Option E is the correct answer.
Strawberries are $2.50 A pound and cantaloupes are $2.25 at the local supermarket. Sally bought 7 pounds of the two kinds of fruit for a family breakfast. If she spent exactly $16.75 and bought at least 1 pound of each fruit how many pounds of fruit did she buy there is no sales tax
Answer:
Sally bought 4 pounds of Strawberries and 3 pounds of Cantaloupes.
Step-by-step explanation:
Let the number of pounds of Strawberries bought by Sally = x
Let the number of pounds of Cantaloupes bought by Sally = y
[tex]\[x + y = 7\][/tex] ---------------------------------(1)
Moreover,
[tex]\[2.5 x + 2.25 y = 16.75\][/tex] ---------------(2)
Solving (1) and (2) by substitution:
[tex]\[x = 7 - y\][/tex]
=> [tex]\[2.5 *(7-y) + 2.25 y = 16.75\][/tex]
=> [tex]\[17.5 - 2.5y + 2.25 y = 16.75\][/tex]
=> [tex]\[0.25y = 0.75\][/tex]
=> [tex]\[y = 3\][/tex]
From (1), x = 7-3 = 4
What term is used to describe the graphical representation of the change in microbial population over time?
Answer:
The term exponential is often used.
Step-by-step explanation:
The term exponential is used to represent changes in population over time. The idea of (positive) exponential is that the higher the number, the higher the growth. You can relate this with a population, because the higher the population, the more opportunities for it to multiply, thus, the higher it grows.
Usually the way to meassure the population of an species after certain number of years x, you use an exponential function of the form
[tex] f(x) = K_0 * a^x [/tex]
For certain constants K₀ and a. K₀ is the initial population at the start of the experiment and a number of exponential growth. Essentially, the population of the species is multiplied by a during each year.
For example, if K₀ = 1000 and a = 2, then the population at the start of the experiment is 1000. After the first year is 1000*2 = 2000 and after the second year it is 2000*2 = 4000. Note that, not only the population grow during the years, but also the amount that the population increases also grow: in the first year it grows 1000, and between the first and second year it grows 2000.
Got three questions need with .
Answer:
14.
Center = (-7,4)
Radius = 7
15. 189 square yards
16. 84 square inches
Step-by-step explanation:
14.
The standard form of a circle is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where
(h,k) is the center
and
r is the radius of the circle
Given, the circle equation in this problem as:
[tex](x+7)^2+(y-4)^2=49[/tex]
We re arrange this:
[tex](x-(-7))^2+(y-(4))^2=7^2[/tex]
Now, we clearly see that the center is (-7,4) and the radius is 7
Hence,
Center = (-7,4)
Radius = 7
15.
For simplicity, let the point at DE, where it makes the right angle, be the point "H".
DEF is the triangle.
So, we see now that:
DE = 21 yd
FH = 18 yd
DE is the base of the triangle and FH is the height of the triangle.
The area of a triangle is:
Area = 0.5 * base * height
So, we now find the area to be:
Area = 0.5 * 21 * 18 = 189 square yards
16.
Rhombus is a quadrilateral (figure with 4 sides) whose 4 sides have equal length.
The diagonal is the length from one corner to the opposite corner. So, a rhombus has 2 diagonals.
The area of the rhombus, in terms of diagonals, would be:
Area = (Diagonal1 * Diagonal2)/2
So, we multiply the 2 diagonal's length and divide the answer by 2.
We have:
Diagonal 1 = 12
Diagonal 2 = 14
Hence, area would be:
Area = (12*14)/2 = 84 square inches
Eddy MS plans to collect more than 3,000 can of food to donate to the EG Food Bank. So far, 500 can have been collected. WRITE an inequality to find the number of can the school can collect on each of the final 5 days to meet their goal.
Answer:
The in equality representing the number of can school can collect each day is [tex]500+5x\geq 3000[/tex].
Eddy MS school has to collect at least 500 cans in each day.
Step-by-step explanation:
Number of cans Eddy has = 500
Number of days left = 5
Target to achieve = 3000
Let number of cans which can be collected in each day be 'x'.
Now we know that;
Number of can he has plus number of can which can be collected in each day multiplied with number of days left should be greater than or equal to 3000
Framing in equation form we get;
[tex]500+5x\geq 3000[/tex]
Hence, The in equality representing the number of can school can collect each day is [tex]500+5x\geq 3000[/tex].
Solving the same we get;
[tex]500+5x\geq 3000[/tex].
Subtracting Both side with 500 using Subtraction property for Inequality we get;
[tex]500+5x-500\geq 3000-500\\\\5x\geq 2500[/tex]
Now Dividing both side by 5 using Division property of Inequality we get;
[tex]\frac{5x}{5}\geq\frac{2500}{5}\\\\x\geq 500[/tex]
Hence Eddy MS school has to collect at least 500 cans in each day.
The entire school of students were surveyed, a total of 950 students. 75% or students said they preferred chocolate ice cream to vanilla. How many students prefer chocolate ice cream?
Answer:
Number of students who prefer chocolate ice cream is approximately 713.
Step-by-step explanation:
Given,
Total number of students = 950
Students who prefer chocolate ice cream = 75%
We have to find out number of students who prefer chocolate ice cream.
For calculating number of students who prefer chocolate ice cream, we have to multiply total number of students with given percentile of students.
Now framing the above sentence in equation form, we get;
Number of students who prefer chocolate ice cream = [tex]950\times75\%[/tex]
Now we have to remove the percentile.
For this we have to divide 75 by 100, we get;
Number of students who prefer chocolate ice cream =[tex]950\times\frac{75}{100}=\frac{71250}{100}=712.50\approx713[/tex]
Hence Number of students who prefer chocolate ice cream is approximately 713.
A train tunnel is modeled by the quadratic function h ( x ) = − 0.18 ^ 2 + 25 , where x is the distance, in feet, from the center of the tracks and h ( x ) is the height of the tunnel, also in feet. Assume that the high point of the tunnel is directly in line with the center of the train tracks.
Round your answers to the nearest tenth as needed.
a) What is the maximum height of the tunnel? feet.
b) How wide is the base of the tunnel? feet.
Answer:
a) 25 feet
b) Base width 23.57 feet
Step-by-step explanation: The expression:
h(x) = -0,18*x² + 25
is a quadratic function ( a parable). as a < 1 open down
The vertex of the parable is V(x,y)
a) V(x) = - b/2a = 0/2a V(x) = 0 to find V(y) we make use of the original equation and plugging x = 0
y = - 0.18*x² + 25 ⇒ y = 0 + 25 ⇒ y = 25
The Vertex is V ( 0 , 25 )
Now vertex in this case is the maximum height.
h(max) = 25 feet
b) To find how wide is the base of the tunnel. We have to consider that for h = 0 we are at ground level therefore the two roots of the quadratic equation will give the wide of the base of the tunnel
Then
h (x) = -018*x² +25 ⇒ 0 = -018*x² +25 ⇒ x² = 25/0.18
x² = 138.89
x = ± 11.79 ft
So we found interception with x axis and wide of the base is
2 * 11.79 = 23.57 feet
In the figure, BP is an angle bisector of ∠CBD.
Find x if m∠1 = 4x - 8 and m∠2 = 3x + 2.
A) 5
B) 7
C) 9
D) 10
Answer:
9
Step-by-step explanation:
In the parallelogram below, W = ?
The value of w in the given figure of parallelogram is, w = 37 degrees.
We can see that the diagonals of the parallelogram divided it into four number of parallelogram.
We know that the sum of all interior angles of a triangle is 180 degrees according to Angle Sum Property of Triangle.
So, from the given figure we can see that in a triangle the interior angles are w, 2w and 69 degrees.
According to Angle Sum Property,
w + 2w + 69 = 180
3w = 180 - 69 = 111
w = 111/3 = 37
Hence the value of w in the given parallelogram is 37 degrees.
To know more about Angle Sum Property here
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Spends a total of $38.75 on 5 drinks and 2 bags of popcorn. Noah spends a total of $37.25 on 3 drinks and 4 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn.
Answer:
3d + 4p = $37.25
5d + 2p = $38.75
Actual Answer:
Bag of popcorn is $5
A drink is $5.75
Step-by-step explanation:
Let drinks = d
Let popcorn = p
Noah: 3d + 4p = $37.25
Other: 5d + 2p = $38.75
Choose a variable to eliminate (We'll choose p)
3d + 4p = $37.25
(5d + 2p = $38.75) -2
Distribute
-10d - 4p = -77.5
The -4p cancels out the 4p, then we combine
-7d = -40.25
Divide both sides by -7
-7d/-7 = -40.25/-7
d = 5.75
Back to 3d + 4p = $37.25
Substitute d with 5.75
3(5.75) + 4p = $37.25
17.25 + 4p = 37.25
Move the constant to the other side
17.25 + 4p = 37.25
-17.25 -17.25
4p = 20
Divide both sides by 4
4p/4 = 20/4
p = 5
June and Stella can each create six floral arrangements in one hour. If they take in 372 Valentineâs Day orders, how many hours will they need to fulfill them?
Answer:
31 hours
Step-by-step explanation:
June and Stella can create 6 floral arrangements in one hour.
They take in 372 Valentine's Day order
No of hours = orders / (June's rate + Stella's rate)
June's rate = 6 arrangements / hour
Stella's rate = 6 arrangements / hour
June's rate + Stella's rate = 2(6 arrangements /hour)
= 12 arrangements / hour
No of hours = 372 arrangements / 12 arrangements / hour
= 31 hours
June and Stella have 31 hours to fulfill the 372 Valentine's Day order
A 15 ft. Ladder is placed against a building so that the distance from the top of the ladder to the ground is 10 ft. Find the distance (to the nearest tenth) from the bottom of the ladder to the building
Answer:
11.2 ft
Step-by-step explanation:
Assuming the building meets the ground at right angles, the right triangle formed has side length 10 ft and hypotenuse 15 ft. Then the other side length (d) is given by the Pythagorean theorem as ...
d² + 10² = 15²
d² = 225 -100 = 125
d = √125 = 5√5 ≈ 11.2 . . . feet
The bottom of the ladder is about 11.2 feet from the building
Terry earns a salary of $36,000 per year. He is paid once per month. He receives a 2.5% pay raise.
How much more money is Terry earning each month?
$25
$75
$90
Answer: $75
Step-by-step explanation:
Since Terry is paid once a month and earns $36000 in a year,
a year = 12 months
To get the amount he is paid in a month we simply divide the $36000 by 12
$36000 / 12 = $3000
In a month he is paid $3000
Now to get the pay raise;
since the pay raise is 2.5 %, we will find 2.5% of $3000
2.5/100 × $3000 = 2.5 × $30 =$75
There Terry receive an increase of $75 in a month