Answer:
See Explanation
Step-by-step explanation:
A prime number is a number that is only divisible by by 1 and itself.Composite numbers on the other hand is any number which is not prime.To determine the number of prime cards needed to build a composite number, we simply express the number as a product of its prime factors.
These are:
4=2X2
6=2X3
8=2X2X2
9=3X3
10=2X5
12=2X2X3
14=2X7
15=3X5
16=2X2X2X2
18=2X3X3
20=2X2X5
21=3X7
22=2X11
24=2X2X2X3
26=2X13
27=3X3X3
28=2X2X7
30=2X3X5
32=2X2X2X2X2
33=3X11
34=2X17
35=5X7
36=2X2X3X3
38=2X19
39=3X13
40=2X2X2X5
42=2X3X7
44=2X2X11
45=3X3X5
46=2X2X13
48=2X2X2X2X3
49=7X7
50=2X5X5
Therefore for each of the numbers, those are the prime number cards to be used.
For the data set 2.5, 6.5, 9, 19, 20, 2.5 what is the mean absolute deviation
Answer:
9
Step-by-step explanation:
it's 9 because you always look in the middle for the mean
The bottom of a ladder must be placed 5 feet from the building. The ladder is 14 feet long. How far above the ground does the ladder touch the wall?
Answer:
3 square roots of 19
Step-by-step explanation:
a squared + b squared = c squared
5 squared + b squared = 14 squared
25 + b squared = 196 squared
b squared = 171
b = square root of 171
b = 3 square roots of 19
hi
If your wall is straight , then. you have a rectangular traingle.
As Pythagoras tells us : wall² = ladder²- ground distance²
wall² = 14²- 5²
wall² = 196 -25
wall² = √171≈13,07
© If you take a number, times by 7 then subtract 1. You get the same as if you took the number,
times by 5 then subtract 8. What is the number?
Answer:
-7/2
Step-by-step explanation:
This question is a word problem.
Step 1: interpretation the question
Let's assume the number is x;
X×7 – 1 = X×5 – 8
7x - 1 = 5x - 8
Step 2. Solve the equation for the unknown.
7x - 1 = 5x - 8
Take like terms together
7x - 5x = - 8 +1
2x = -7
Divide both sides by 2
x = -7/2
The answer is -7/2
If the height of the parallelogram shown is decreased by 1 inch and the base is decreased by 2 inches, what is the area of the new parallelogram?
a. 108in2
b. 104in2
c. 78in2
d. 84 in2
Answer:
B
Step-by-step explanation:
you multiply the numbers and remember the little square is 90
The area of new parallelogram is 78in2
The original parallelogram has a base of 18 inches and a height of 10 inches. Therefore, its area is 18 x10 = 180 square inches.If the height is decreased by 1 inch and the base is decreased by 2 inches, the new base will be 18 - 2 = 16 inches and the new height will be 10 - 1 = 9 inches. So, the area of the new parallelogram will be 16 x 9 = 144 square inches.Therefore, the answer is c. 78in2.
Here's a breakdown of the reasoning for each option:a. 108in2: This is incorrect because it's smaller than the area of the original parallelogram, even though both the base and height are decreased.b. 104in2:
This is also incorrect because it's still larger than the area of the new parallelogram.c. 78in2:
This is the correct answer, as calculated above.d. 84 in2: This is incorrect because it's closer to the area of the original parallelogram than the new one.
What is the volume of the prism? Length 8ft height 12ft width 6ft
Answer:
[tex]\huge\boxed{V=576\ ft^3}[/tex]
Step-by-step explanation:
[tex]\text{The formula of a volume of a prism with dimensions}\ l\times w\times h:\\\\V=lwh.\\\\\text{We have}\\\\l=8ft,\ w=6ft,\ h=12ft.\\\\\text{Substitute:}\\\\V=(8)(6)(12)=576(ft^3)[/tex]
The point M(-6,8) is the midpoint of AB. The point A has coordinates (-2,10). What are the coordinates of B
Answer:
m/6-8 =m/58
Step-by-step explanation:
Using the midpoint formula, the coordinates of point B are determined by setting up equations with the known coordinates of point A and midpoint M. Solving these equations yields the x-coordinate of B as -10 and the y-coordinate as 6, making the coordinates of point B (-10, 6).
Explanation:The question is asking to determine the coordinates of point B if M(-6,8) is the midpoint of AB and A has coordinates (-2,10). To find the coordinates of B, we use the midpoint formula which states that the midpoint M(x,y) is given by M = ((x1 + x2)/2, (y1 + y2)/2) where (x1, y1) and (x2, y2) are the coordinates of points A and B respectively. Since we know the coordinates of A and M, we can set up equations to solve for the coordinates of B.
To find the x-coordinate of B, we set up the equation -6 = (-2 + xB)/2 which yields xB = -10. For the y-coordinate, we use the equation 8 = (10 + yB)/2 which gives us yB = 6. Therefore, the coordinates of point B are (-10, 6).
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Rebecca said that the graph is NOT a function. What is the BEST reason she could give to Mr. Bradley to support her statement?
A) The graph is not symmetrical about the y-axis
B) Every value of y has a single value of x
C) A vertical line placed on the graph could intersect more than one point
D) Every value of x has a single value of y
Answer:
choose choice C.
Step-by-step explanation:
many vertical lines can cross this graph more than once, which defies the definition of a function.
Answer:
c) A vertical line placed on the graph could intersect more than one point
Step-by-step explanation:
if you did the vertical line test, you would see that there would be more than one point per value.
hope i helped:) !!!
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Line x and line z are straight lines. Lines x, z, and y intersect to form 5 angles. From top left, clockwise, the angles are: a: right angle, b, c, d, e. Which pair of angles are vertical? Angle a and Angle d Angle b and Angle d Angle a and Angle b Angle c and Angle e
Answer: C AND E
Step-by-step explanation:
Option D is correct, Angle c and Angle e are vertical angles.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given that Line x and line z are straight lines.
Lines x, z, and y intersect to form 5 angles. From top left, clockwise, the angles are: a: right angle, b, c, d, e.
Vertical angles are opposite to each other and not adjacent.
In this case, angle c and angle e are opposite to each other, as they are on opposite sides of the intersection between lines y and z, and they are not adjacent to each other. Therefore, they must be vertical angles.
Hence, Option D is correct, Angle c and Angle e are vertical angles.
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The parent function f(x) = 1.5x is translated such that the function g(x) = 1.5x + 1 + 2 represents the new function. Which is the graph of g(x)? On a coordinate plane, an exponential function increases from quadrant 2 to quadrant 1. It crosses the y -axis at (0, 2.5). On a coordinate plane, an exponential function increases from quadrant 3, through quadrant 4, to quadrant 1. It crosses the y-axis at (0, negative 0.5). On a coordinate plane, an exponential function increases from quadrant 3, through quadrant 4, to quadrant 1. It crosses the y-axis at (0, negative 1.5). On a coordinate plane, an exponential function increases from quadrant 2 to quadrant 1. It crosses the y -axis at (0, 3.5).
Answer:
Its the fourth graph
Step-by-step explanation:
i got it right
Answer: the 4th one
Step-by-step explanation:
i just did this
Which number is represented by point E on the graph?
Answer:
It'll be -0.25
Step-by-step explanation:
Notice how it is to the left of zero, anything to the left of zero is negative. With that in mind, we can eliminate A. The half mark between 0 and -1 represents 0.50, and since it goes by quarters, the E is at the first quarter, which is 0.25. Hopefully this helps!
Ella already knew 5 appetizer recipes before starting culinary school, and she will learn 2 new
appetizer recipes during each week of school. Write an equation that shows the relationship
between the number of weeks w and the number of appetizer recipes a.
Write your answer as an equation with a first, followed by an equals sign.
A = 2w+5
example: on week three, she would have the recipes from the other weeks that you have to account for as well as the extra five
2(3)+5=11 so A would equal 11 by week three.
Use multiplication because it is essentially repeated addition.
2(from week 1) + 2(from week 2) + 2(from week 3) + 5(prior to school) =11
What are the roots of the polynomial equation?
Answer:
The roots of the polynomial equation in this case would be the intersection of the 2 polynomial functions. which are at x = 4 and x = -3
Step-by-step explanation:
The roots are found by finding the x-values of the intersections of these two cubic polynomial functions.
We could try solving algebraically, but you have the graph.
SE
LAILLIU
A six-sided die is rolled 50 times.
The number 4 appears 18 times.
What is the experimental probability
of getting a four?
A .08
B 17
C.32
D.36
Answer:
D.36
Step-by-step explanation:
The experimental probability of an outcome is the the number of experients in which this outcome happened divided by the total number of experiments.
In this problem:
The number 4 appeared 18 times in 50 experiments.
So the experimental probability of getting a four is 18/50 = 0.36.
So the correct answer is:
D.36
Compensation professionals in XYZ Company use regression analysis to determine the pay rates of its marketing professionals. There are 4 different marketing job titles in XYZ Company. Compensation professionals use job evaluation points assigned to each marketing job title and a salary survey data. In other words, they regress job evaluation points on the salary data. What does it mean when the R2 value of this regression turns out to be 0.85
Answer: This means that the salaries of their marketing professionals are not closely related to their job titles. In further explanation, this shows that a professional with a higher job title, may be paid a lower salary when compared to a professional with a lower job title.
A 0.85 R-Squared shows that the points are far from the trend lines. From this, we can assume that the marketing professionals are paid base on commission on sales, and not base on job position.
Step-by-step explanation: R-Squared is a measure used in statistics, to represent how much proportion of the dependent variables that is explained by the independent variables. A high value of R^2 shows a very low correlation between the dependent and independent variables, while a low value of R^2 shows that the dependent and independent variables are closely related. The R-Squared value are a measure of percentage value.
31) Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. a. There is not sufficient evidence to support the claim that the mean is greater than 32 miles per gallon. b. There is not sufficient evidence to support the claim that the mean is less than 32 miles per gallon. c. There is sufficient evidence to support the claim that the mean is less than 32 miles per gallon. d. There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
Answer:
Option D is correct.
Rejecting the null hypothesis means that;
There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
For this question, Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. And since this is talking distance covered per gallon of fuel, better means that the new sedan will average more than 32 miles per gallon.
So, the null hypothesis negating this claim would be that there isn't significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
That is, the new average will be less than or equal to 32 miles per hour.
And the alternative hypothesis will confirm the claim that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 32 miles per gallon
The alternative hypothesis is given as
Hₐ: μ > 32 miles per gallon
So, after the hypothesis test has been conducted, rejecting the null hypothesis means accepting the alternative hypothesis and its statement that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
Hence, option D is correct.
Hope this Helps!!!
The conclusion of the hypothesis test indicates that there is sufficient evidence to support the claim that the mean fuel efficiency of the new Libra sedan is greater than 32 miles per gallon.
Explanation:From the noun hypothesis testing conducted, the conclusion drawn is to reject the null hypothesis. In non-technical terms, rejecting the null hypothesis means that based on the data collected and analyzed, there is sufficient statistical evidence to support the claim that contrary to the null hypothesis, the average (or 'mean') miles per gallon of the new Libra sedan is indeed greater than 32 miles per gallon. These results should confirm Carter Motor Company's assertions about their vehicle's fuel efficiency.
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Find the distance between (3, 24) and (7,
56).
Answer:
Square root of 1040
Decimal form - 32.249
Step-by-step explanation:
The distance between the endpoints (3, 24) and (7, 56) will be 32.25 units.
What is the distance between two points?Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
The two endpoints are given below.
(3, 24) and (7, 56)
Then the distance between the endpoints (3, 24) and (7, 56) will be
D² = (7 - 3)² + (56 - 24)²
D² = 4² + 32²
D² = 16 + 1024
D² = 1040
D = 32.25 units
The distance between the endpoints (3, 24) and (7, 56) will be 32.25 units.
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If f(x)=4x+1 and g(x) = x^2-5 find (f-g)(x)
Answer:
-x^2 + 4x + 6
Step-by-step explanation:
(f-g)(x) = f(x) - g(x) =
4x + 1 - (x^2 -5) =
-x^2 +4x + 6
Find the measures of angels of M and N
M (6y-10)
N (4y-10)
We have been given an image of a trapezoid. We are asked to find the measure of angle M and N.
We know that bases of trapezoid are parallel and the two angles between two parallel lines are supplementary, so we can set an equation as:
[tex]\angle M+\angle N=180[/tex]
[tex](6y-10)+(4y-10)=180[/tex]
[tex]6y-10+4y-10=180[/tex]
[tex]10y-20=180[/tex]
[tex]10y-20+20=180+20[/tex]
[tex]10y=200[/tex]
[tex]\frac{10y}{10}=\frac{200}{10}[/tex]
[tex]y=20[/tex]
Upon substituting value of y in measure of angle M, we will get:
[tex]m\angle M=6y-10[/tex]
[tex]m\angle M=6(20)-10[/tex]
[tex]m\angle M=120-10[/tex]
[tex]m\angle M=110[/tex]
Therefore, measure of angle M is 110 degrees.
Similarly, we will find the value of angle N as:
[tex]m\angle N=4y-10[/tex]
[tex]m\angle N=4(20)-10[/tex]
[tex]m\angle N=80-10[/tex]
[tex]m\angle N=70[/tex]
Therefore, measure of angle N is 70 degrees.
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 7.8 parts/million (ppm). A researcher believes that the current ozone level is not at a normal level. The mean of 16 samples is 8.2 ppm with a standard deviation of 0.6. Assume the population is normally distributed. A level of significance of 0.01 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
The value of the test statistic is [tex]t = 2.67[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} = 7.8[/tex]
The alternate hypotesis is:
[tex]H_{1} \neq 7.8[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem, we have that:
[tex]X = 8.2, \mu = 7.8, \sigma = 0.6, n = 16[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{8.2 - 7.8}{\frac{0.6}{\sqrt{16}}}[/tex]
[tex]t = 2.67[/tex]
The value of the test statistic is [tex]t = 2.67[/tex]
A marketing research company needs to estimate which of two medical plans its employees prefer. A random sample of n employees produced the 95% confidence interval (0.366 comma 0.506 )for the proportion of employees who prefer plan A. Identify the point estimate for estimating the true proportion of employees who prefer that plan.
Answer:
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Step-by-step explanation:
A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
In this problem, we have that:
Lower bound: 0.366
Upper bound: 0.506
Point estimate:
(0.366 + 0.506)/2 = 0.436
The point estimate for estimating the true proportion of employees who prefer that plan is 0.436
Answer:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
Step-by-step explanation:
We define the parameter of interest as the proportion of employees who prefer plan p and we want to estimate this true parameter
The confidence interval for the this proportion is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
After calculate the 95% confidence interval we got (0.366, 0.506)
We can obtain the best estimate for the proportion of employees who prefer plan like this:
[tex]\hat p =\frac{Upper +Lower}{2}[/tex]
Where Upper and Lower represent the limits for the confidence interval and replacing we got:
[tex]\hat p = \frac{0.366+0.506}{2}= 0.436[/tex]
And the point of estimate for the proportion of employees who prefer plan is on this case 0.436 or 43.6%.
The margin of error can be estimated using the fact that this confidence interval is symmetrical and we got:
[tex]ME=\frac{Upper-Lower}{2}= \frac{0.506-0.366}{2}=0.07[/tex]
answer question pls
Answer:
B,1/5
Step-by-step explanation:
Answer:
the answer would be
B aka your second option
Step-by-step explanation:
i don't really have a step by step but this is the first question i've answered on this app let me know if i am helpful!!
A roof on a castle tower is shaped like a cone with a diameter of 12 feet and has a slant height of 13 feet one bundle of Shingles covers 32 ft.² how many bundles should you buy to cover the roof
Answer:
8
Step-by-step explanation:
The lateral area of a cone is ...
LA = (π/2)ds
where d is the diameter, and s is the slant height.
The area of this tower roof is about ...
LA = (π/2)(12 ft)(13 ft) = 78π ft² ≈ 245 ft²
About 245/32 = 7.7 bundles of shingles will be required for coverage.
You should buy 8 bundles of shingles to cover the roof.
what is the value of 6+ {[3x(13-5)]-2}
Answer:
28 you have to do it from left to right
Answer:
13-5=8
3x8=24
24-2=22
22+6=28
28 is your answer
Step-by-step explanation:
What is the surface area
Suppose that you found two different solutions for a system of two linear equations. How many solutions must the system have?
Answer:
One solution.
Step-by-step explanation:
A linear line only goes one way, and thus, two lines can only meet at one point.
That is unless, the linear equations are both the same, then they will have infinite solutions.
But what you're asking is if they're different so no, you cannot have two solutions for a system of two linear equations.
Answer:
0
Step-by-step explanation:
Two different solutions means the two equations aren't consistent - there's no unique solution that solves the whole system. Two lines can meet at at most one point, so in this case, no solution to the first equation will be a solution to the second. The system has 0 solutions.
Simplify: (−7x + 5) – (2x2 – 8x + 6)
Answer:
2x^2 + x -1
Step-by-step explanation:
-7x + 5 - 2x^2 + 8x -6
2x^2 + x -1
34. The sum of the lengths of the two bases of a trapezoid
is 22 cm, and its area is 66 cm". What is the height of
the trapezoid?
Answer:
h=6
Step-by-step explanation:
the formula for a trapezoid’s area is to multiply the bases (a and b) by the height of the trapezoid, then divide it all by 2.
so typed out, that would look like:
((a+b) h) / 2
and in the case of this problem:
((22) h) / 2 = 66
so just go ahead and solve it algebraically from there and you’re good!
Help! Best answer = Brainiest!
Which of the following statements is false?
a. R3 is a vector space
b. P2 is a vector space
C. M2x2 is a vector space
d. The set of all polynomials of degree 4 is a vector space
Answer:
C . M2x2 is a vector space
Step-by-step explanation:
According to the definition, the each element in a vector spaces is a vector. So, 2×2 matrix cannot be element in a vector space since it is not even a vector.
The set of all ordered triples of real numbers is called 3‐space, denoted R 3 (“R three”). See Figure . ... Vectors in R 3 are called 3‐vectors (because there are 3 components), and the geometric descriptions of addition and scalar multiplication given for 2‐vectors also carry over to 3‐vectors.
Since every polynomial of degree up to 2 is also a polynomial of degree up to 3, P2 is a subset of P3. And we already know that P2 is a vector space, so it is a subspace of P3.
With addition, the set of polynomials of degree 2 almost form a vector space, but there are some problem. The first one, is that the zero vector, i.e. the zero polynomial is not of degree 2. ... If you really need them to form a vector space, then you should consider the set of all polynomials of degree at most 2.
En un platillo de una balanza colocamos un queso, en el otro ponemos las tres cuartas partes de otro queso igual y para equilibrarlo añadimos un peso de tres cuartos de kilo. ¿Cuál es el peso del queso?
Answer: The cheese weighs 3 kilograms.
Step-by-step explanation:
I will answer this in English, feel free to translate it if you need it.
This can be translated to:
In a weighing pan of a scale, we place a cheese, in the other we put three-quarters of another cheese equal, and to balance it we add a weight of 3/4 kg. What is the weight of the cheese?
We know that the weight on both pans must be the same.
Then if the weight of the cheese is C, we have the equation:
C = (3/4)*C + 3/4kg
this says:
The weight of the complete cheese is equal to the weight of 3/4 of the cheese plus 3/4kg.
Now we can solve it for C.
C - (3/4)*C = 3/4kg
C*(1 - 3/4) = C*(1/4) = 3/4kg
C = 4*(3/4)kg = 3kg
The cheese weighs 3 kilograms.