Answer:
163/500 = 0.326
Step-by-step Explanation:
Drawing a Venn diagram for this, we will have 3 circles. One will represent rock, one will represent country, and one will represent jazz.
There are 11 students that like all 3 types of music. This means the number 11 goes in the intersection of all 3 circles.
There are a total of 30 students that like rock and country; taking out the 11 that like all 3, this leaves 30-11 = 19 students in the intersection of just rock and country.
There are a total of 27 students that like rock and jazz; taking out the 11 that like all 3, this leaves 27-11 = 16 students in the intersection of just rock and jazz.
There are a total of 22 students that like country and jazz; taking out the 11 that like all 3, this leaves 22-11 = 11 students in the intersection of just country and jazz.
There are 206 students that like rock; taking out the 11 that like all 3, the 19 that like rock and country, and the 16 that like rock and jazz, we have
206-(11+19+16) = 206-(46) = 160 in just rock.
There are 161 students that like country; taking out the 11 that like all 3, the 19 that like rock and country, and the 11 that like country and jazz, we have
161-(11+19+11) = 161-(41) = 120 in just country.
There are 118 students that like jazz; taking out the 11 that like all 3, the 16 that like rock and jazz, and the 11 that like country and jazz, we have
118-(11+16+11) = 118-38 = 80 in just jazz.
This leaves
500-(80+120+160+11+11+19+16) = 500-417 = 83 students that like none of the 3 types of music.
This means for the probability that a student likes neither rock nor country, they either like just jazz or none of the 3; this is (83+80)/500 = 163/500 = 0.326.
The probability that a randomly selected student likes neither rock nor country is;
P(R' ∩ C') = 0.326
Let us denote them as follows;
Number that like rock music be R
Number that like Country music be C
Number that like Jazz music be J
Thus, as we are given we have;
R = 206
C = 161
J = 118
R ∩ C = 30 - 11 = 19
R ∩ J = 27 - 11 = 16
C ∩ J = 22 - 11 = 11
R ∩ C ∩ J = 11
Thus, number that liked only jazz music is;n(only jazz) = J - [(R ∩ J) + (C ∩ J) + (R ∩ C ∩ J)]
n(only jazz) = 118 - (16 + 11 + 11)
n(only J) = 80
Number of students that liked only Rock music;n(only Rock) = R - [(R ∩ C) + (R ∩ J) + (R ∩ C ∩ J)]
n(only Rock) = 206 - (19 + 16 + 11)
n(only R) = 160
Number of students that liked only country music;n(only country) = C - [(R ∩ C) + (C ∩ J) + (R ∩ C ∩ J)]
n(only country) = 161 - (19 + 11 + 11)
n(only C) = 120
Now, the number of students that like neither of the 3 music is;
A' ∩ B' ∩ C' = 500 - [(R ∩ C) + (R ∩ J) + (C ∩ J) + (R ∩ C ∩ J) + n(only J) + n(only R) + n(only C)]
⇒ 500 - (80 + 120 + 160 + 19 + 16 + 11 + 11)
⇒ A' ∩ B' ∩ C' = 83
Thus, number of students that likes neither rock nor country is;
n(A' ∩ B') = (A' ∩ B' ∩ C') + n(only C)
n(A' ∩ B') = 83 + 80
n(A' ∩ B') = 163
Thus, probability that a randomly selected student likes neither rock nor country = 163/500 = 0.326
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Formulate the quadratic function that contains the points (-1,2), (0,-1) and (2,5).
1.) f(x) = 2x^2 + x + 1
2.) f(x) = 2x^2 - x - 1
3.) f(x) = 2x^2 - x + 2
4.) f(x) = 2x^2 - x - 2
Answer:
option 2
2x²- x - 1
Step-by-step explanation:
We are given points: (-1,2), (0,-1) and (2,5)
Substitute each point one by one in the quadratic equation to check if the quadratic equation contains all points mention.
2) f(x) = 2x²- x - 1
Point(-1,2)
f(-1) = 2(-1)² -(-1) -1
2 = 2 + 1 - 1
2 = 2
Point(0,-1)
f(0) = 2(0)² -(0) -1
-1 = 0 - 0 -1
-1 = -1
Point(2,5)
f(2) = 2(2)² -(2) -1
5 = 8 - 2 -1
5 = 6 - 1
5 = 5
I think I got everything but the c part. Can someone help me
you got everything right
A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant comma consonant comma vowel comma consonant comma number comma numberconsonant, consonant, consonant, vowel, consonant, number, number (for example, inpray 93inpray93). Assume that repeats are allowed. Complete parts (a) and (b). (a) Assuming passwords are not case sensitive, how many such passwords are possible (assume that there are 5 vowels and 21 consonants)?
The password format is = inpray93
vowel , consonant, consonant, consonant, vowel, consonant, number, number.
There are 21 consonants, 5 vowels and 10 number choices (0-9)
Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).
Passwords are not case sensitive which means upper case and lower case letters are same.
So, the number of passwords can be =
[tex]5\times21\times21\times21\times5\times21\times10\times10[/tex]
= 486202500
Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.
This means all the letters are different.
So, number of passwords will be =
[tex]10\times42\times42\times42\times10\times42\times10\times10[/tex]
= 31116960000
Find the difference between the fastest girls time and the slowest girl time. Barbra ran 3 3/10, Donna ran 2 4/5 , Cindy ran 4 3/5 and Nicole ran 2 1/10
Answer: 2.5 or 2 1/2
Step-by-step explanation:
You can convert the mixed fractions to decimal numbers:
- Divide the numerator by the denominator of the fraction.
- Add the result to the whole number.
Thenyou have:
Barbara's time: [tex]3\ 3/10=3+0.3=3.3[/tex]
Donna's time: [tex]2\ 4/5=2+0.8=2.8[/tex]
Cindy's time: [tex]4\ 3/5=4+0.6=4.6[/tex]
Nicole's time: [tex]2\ 1/10=2+0.1=2.1[/tex]
As you can see, the fastest girl is Cindy and the slowest girl is Nicole.
Then, you must make the following subtraction to calculate the difference:
[tex]4.6-2.1=2.5[/tex] or 2 1/2
Answer:
Cindy's correct time is 3 2/5 (for the portfolio assignment that this question goes with).
Step-by-step explanation:
Jack’s favorite colors are blue and red.
He has 2 blue shirts, 1 red shirt, 1 blue jacket, 1 red belt, 1 blue pair of pants and 1 red pair of pants.
Jack selects one of these garments at random. Let A be the event that he selects a blue garment and B be the event that he chooses a belt.
What is the probability that the garment Jack chooses is either blue or a belt?
Answer:
5/7 or 71%
Step-by-step explanation:
4/7 (blue) + 1/7 (belt) = 5/7
Answer: Probability of event A = 0.57
Probability of event B = 0.14
Step-by-step explanation:
The data is:
2 blue shirts
1 red shirt
1 blue jacket
1 red belt
1 blue pair of pants
1 red pair of pants
the total number of garments is: 2 + 1 + 1 + 1 + 1 + 1 = 7
the number of blue ones is: 2 + 1 + 1 = 4
the number of belts is: 1
then, the probability of selecting at random one blue garment is equal to the number of blue ones divided the total number:
Pa = 4/7 =0.57
the probability of selecting the belt is equal to the number of belts divided the total number of garments, this is:
Pb = 1/7 = 0.14
Jimmy is planning to paint the gate of his house. The gate has a glass panel. Painting the gate costs $2.50 per square foot. How much will he have to spend to paint the gate? PLEASE HELP!!
Answer: Third option.
Step-by-step explanation:
Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.
The formula for calculate the area of a trapezoid is:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where h is the height, B is the larger base and b is the smaller base.
In this case:
[tex]B=10ft\\b=7ft\\h=5ft[/tex]
Substituting, you get:
[tex]A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2[/tex]
Calculate the area of the rectangular glass panel, with the formula:
[tex]A_{panel}=l*w[/tex]
Where the lenght is [tex]l=1.43ft[/tex] and the width is [tex]w=0.71ft[/tex]
Then:
[tex]A_{panel}=(1.43ft)(0.71ft)=1.01ft^2[/tex]
The area he needs to paint is:
[tex]A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2[/tex]
If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:
[tex]=(41.49)(\$2.50)\\=\$103.725[/tex]
Therefore the answer is the third option.
To calculate the cost of painting the gate, find the area of the glass panel by multiplying its length and width. Multiply the area by the cost per square foot to find the total cost.
Explanation:To calculate the cost of painting the gate, we need to find the area of the glass panel first. Let's say the length of the panel is 'l' feet and the width is 'w' feet. The area of a rectangle is given by the formula A = l × w. Once we have the area, we can multiply it by the cost per square foot ($2.50) to find the total cost. So the formula to calculate the cost of painting the gate is: Cost = Area × Cost per square foot. Substitute the values you know into the formula and solve for the cost.
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There are 3 cups each cup is full with 5/8 of water how much water is their in all
1 cup = 8 ounces
so you'll have 5 ounces in each cup
5/8+5/8+5/8=15/8 (roughly 15 ounces or just under 2 cups of water)
Hayden bought 48 new trading cards.Three fourths of the new cards are baseball cards.How many baseball cards did hayden buy?
Answer:
36
Step-by-step explanation:
1. 48 divided by 3= 12
2. 12 x 3= 36
You estimate you can do 12 math problems in 45 minutes. How long should it take you to do 20 math problems?
[tex]\bf \begin{array}{ccll} problems&minutes\\ \cline{1-2} 12&45\\ 20&x \end{array}\implies \cfrac{12}{20}=\cfrac{45}{x}\implies \cfrac{3}{5}=\cfrac{45}{x}\implies 3x=225 \\\\\\ x=\cfrac{225}{3}\implies x=75[/tex]
It takes 75 minutes to solve 20 math problems.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here it takes 45 minutes to solve 12 math problems thus to solve 1 math problem it will take t= 45/12
=3.75 minutes
Thus to solve 20 math problems it will take t₂₀=3.75×20
=75 minutes
Hence, It takes 75 minutes to solve 20 math problems.
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Please help me with this problem
Diagonal = SQRT(8^2 + 12^2 + 30^2)
Diagonal = SQRT(64 + 144 + 900)
Diagonal = SQRT(1108)
Diagonal = 33.3 feet
A circle is divided into 9 equal parts. What is the angle measured of two of those parts?What is the degrees
Answer:
Angle of 1 part: 40°
Angle of 2 parts: 80°
Step-by-step explanation:
Angles in a circle / Equal parts of a circles = Angle of 1 part
360/9 = 40°
40 x 2 = 80
A shoe store is selling a pair of shoes for $60 that has been discounted by 20%. What was the original selling price? Show your work.
Answer:
The original selling price was [tex]\$75[/tex]
Step-by-step explanation:
Let
x-----> the original selling price
we know that
[tex]100\%-20\%=80\%=80/100=0.80[/tex]
so
[tex]0.80(x)=60[/tex] -----> equation that represent the situation
solve for x
Divide by 0.80 both sides
[tex]x=60/0.80=\$75[/tex]
The weights of tomatoes in a bin are normally distributed with a mean of 120 grams and a standard deviation of 4.3 grams. Approximately 40% of the tomatoes weigh less than which amount?
A. 111 g
B. 114 g
C. 117 g
D. 119 g
Answer:
the answer is 119g
Step-by-step explanation:
x-120/4.3=-0.25
x-120=-1075
x=118.925=119g
Approximately 40% of the tomatoes weigh less than 119 g.
The correct answer is option D.
What is z-score?A z-score also called a standard score is a measure of how many standard deviations a data point is away from the given mean of a distribution.
It measures the unusual or extreme a particular data point is compared to the rest of the distribution
We have,
To solve this problem, we can use the cumulative distribution function (CDF) of the normal distribution.
The CDF gives the probability that a random variable is less than or equal to a given value.
Given that the mean of tomato weight is 120 grams and the standard deviation is 4.3 grams,
We can use this information to find the probability that a randomly selected tomato weighs less than a certain amount.
Let's calculate the z-score for each option:
A. 111 g:
z-score = (111 - 120) / 4.3 ≈ -2.093
B. 114 g:
z-score = (114 - 120) / 4.3 ≈ -1.395
C. 117 g:
z-score = (117 - 120) / 4.3 ≈ -0.698
D. 119 g:
z-score = (119 - 120) / 4.3 ≈ -0.233
Now, we can use a standard normal distribution table or a calculator that provides the cumulative distribution function (CDF) of the standard normal distribution to find the probability corresponding to each z-score.
The option with the highest probability, or approximately 40%, is the correct answer.
Based on the calculations, it appears that option D. 119 g has the highest probability of approximately 40% for a tomato weighing less than that amount.
Thus,
Approximately 40% of the tomatoes weigh less than 119 g.
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A parallelogram has sides of 18 and 26 ft, and an angle of 39° . Find the shorter diagonal
Answer:
16.51
Step-by-step explanation:
In a parallelogram, the opposite angles are always equal in measure. So two of the angles in the parallelogram measure 39 degrees each.
The sum of angles of the parallelogram must be 360 degrees. Let the other two angles be x degree each. We can set up the following equation for the angles:
39 + 39 + x + x = 360
78 + 2x = 360
2x = 282
x = 141
This means, the other two angles measure 141 degree each. The shorter diagonal will be opposite to the shorter angle.
Hence, the diagonal opposite to the angle 39 degree will be the shorter one. A diagonal divides the parallelogram in two triangles. So we will have two sides and an included angle and we have to find the third side of the triangle which can be found using the law of cosines. Let the third side be c as shown in image below, using the law of cosines, we can write:
[tex]c^{2} = a^{2}+ b^{2} -2ab cos(\gamma)\\\\c^{2}=18^{2}+26^{2}-2(18)(26)cos(39)\\\\ c^{2}=272.59\\\\ c=16.51[/tex]
Thus the shorter diagonal will be 16.51 feet in measure.
To find the shorter diagonal of a parallelogram with given side lengths and angle, use the formula √(a^2 + b^2 - 2abcosθ).
Explanation:To find the shorter diagonal of a parallelogram, we need to use the formula:
Shorter diagonal = √(a^2 + b^2 - 2abcosθ)
Where a and b are the sides of the parallelogram and θ is the angle between them.
Using the given information, we have a = 18 ft, b = 26 ft, and θ = 39°.
Substituting these values into the formula, we get:
Shorter diagonal = √(18^2 + 26^2 - 2(18)(26)cos(39°))
Calculating this expression gives us:
Shorter diagonal ≈ 9.15 ft
In Amy's garden the ratio of herbs to plants is 5:2. If there are 40 herb plants, how many vegetable plants are in her garden?
Please help! Will give the brain thing! 40 points.
Simplify each Polynomial Expression:
1. 2x(-3x - 1)
2. -x(4 + 2x)
3. -5x(-2x + 4)
4. x(-2x - 2) + 3(-4x - 6x)
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
You just distribute (multiply) what's outside the parentheses with everything inside the parentheses. Then, combine like terms.
Answer:
1. 2x(-3x - 1)
-6x^2 - 2x
2. -x(4 + 2x)
-4x - 2x^2
3. -5x(-2x + 4)
10x^2 - 20x
4. x(-2x - 2) + 3(-4x - 6x)
-2x^2 - 2x - 12x - 18x
-2x^2 - 32x
5. 2xy(-3x - 5y) + 4y(-2xy - 4x)
-6x^2y - 10xy^2 -8xy^2 - 16yx
-6x^2y -18xy^2 - 16yx
What is the measure of EFG?
Answer: [tex]149^{\circ}[/tex]
Step-by-step explanation:
From the given figure, the measure of central angle FDG is given by :-
[tex]\angle{EDG}=\angle{EDF}+\angle{FDG}\\\\=83^{\circ}+66^{\circ}\\\\=149^{\circ}[/tex]
We know that the measure of arc in degrees is equals the measure of the central angle that intercepts the arc.
Now,the measure of arc EFG is given by :-
[tex]Arc\ \text{EFG}=\text{Central angle EDG}=149^{\circ}[/tex]
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
log7=0.8451 log5=0.6990
log3=0.4771 log2=0.3010
log12
Answer:
B
Step-by-step explanation:
We can use the logarithm property shown below to evaluate this:
[tex]Log(x*y*z)=logx+logy+logz[/tex]
Now we can write Log 12 as Log (2*2*3).
Using the rule, we can write:
Log (2*2*3) = Log 2 + Log 2 + Log 3
We are given values of Log 2 and Log 3, plugging these we get:
Log (2*2*3) = Log 2 + Log 2 + Log 3
Log (2*2*3) = 0.3010 + 0.3010 + 0.4771 = 1.0791
Answer choice B is right.
We can factor out 12 using 2 and 3.
log(12) = log(2^2 * 3)
Rewrite it using the product rule [ log(xy) = log(x) + log(y) ]
log(2^2 * 3) = 2 log(2) + log(3)
Simplify using the given values.
2(0.3010) + 0.4771
0.602 + 0.4771
1.0791
Therefore, the answer is b. ≈ 1.0791
Best of Luck!
The expanded form of a number is (4 × 1) + (2 × 0.01). Which shows another way to write the number?
Answer:
4.02
Step-by-step explanation:
4+0.02=4.02
The number represented by the expanded form (4 × 1) + (2 × 0.01) can be presented in other forms such as decimal form (4.02), fraction form (402/100), percentage form (402%), or scientific notation (4.02 x 100).
Explanation:The expanded form of a number is a way of breaking down the number into its parts. In this specific question, the expanded form of the number given is (4 × 1) + (2 × 0.01). This form shows the number 4.02 in a decomposed format. To write the number 4.02 in another format, we can use the decimal form, fraction form, percentage form, or even scientific notation.
For instance:
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Twice Jack's age plus 5 is 21. Write and solve an equation. How old is Jack? A) 8 B) 13 C) 32 D) 52
Answer:
A - 8
Step-by-step explanation:
(21-5)/2
16/2 = 8
Answer: Jack is 8 years old (option A)
Step-by-step explanation:
Hi, to answer this question we have to write an equation using the information given:
Twice Jack's age plus 5 is 21Twice : Means that the age of jack (j) is multiplied by 2 (2j),
Plus 5: we have to add 5 (2j+5).
Is 21: all is equal to 21.
Mathematically speaking:
2j +5 =21
Solving:
2j =21-5
2j =16
j= 16/2
j=8
Option A). 8
Feel free to ask for more if needed or if you did not understand something.
A triangle has a perimeter of 206 inches. if the two sides of the triangle measure 59 inches and 94 inches, determined the length of other side.
➷ The perimeter is the sum of all the lengths
206 - (59 + 94) = 53
It is 53 inches.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
53 inches.
Step-by-step explanation:
Perimeter = sum of the 3 sides so the third side
= 206 - 94 - 59 = 53.
Solve for x ... x/6 = 2
Answer:The answer is x=12
Step-by-step explanation: 2*6=12 and 12/6=2
Answer:
x = 12
Step-by-step explanation:
12/6 = 2
Factorise 36x - 16 please :)
Answer:
4(9x-4)
Step-by-step explanation:
➷ Find the greatest common factor between the two values:
In this case, it is 4
This value will go outside the parenthesis
Divide each of the values by 4:
36x/4 = 9x
-16/4 = -4
The final answer is 4(9x - 4)
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
In the sum of two numbers is 15 and the product is 56, what are the two numbers?
ANSWER:
HOPE IT HELPED YOU ☺
Use the figure below to find the Measure of Angle BEH
Explain/Show how you got your answer please
Answer:
The answer is ; m∠BEH = 55°
Step-by-step explanation:
(17.33) A randomized comparative experiment examined the effect of a technique for improving one’s ability to focus one’s attention on performance of undergraduate students on the Verbal portion of the Graduate Record Exam (GRE). The researchers found a statistically significant improvement in performance on the Verbal GRE (P = 0.05). When asked to explain the meaning of (P =0.05) a student says, “This means there is only probability equal to 0.05 that the null hypothesis is true.” Explain what P= 0.05 really means in a way that makes it clear that the student's explanation is wrong. P = 0.05 means that the outcome is at least 5% higher among one group than among the other group. P = 0.05 means that there is a probability of 0.05 that the null hypothesis is false. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05. P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is less than 0.05.
Answer:
See below
Step-by-step explanation:
What the significance level tells us is that, in this case, there is only a 5% chance that the change in results from the sample happened by random chance. So that means that most likely the change in results did not happen by random change, and something happen between the times the samples were taken. In this case, the experiment.
P = 0.05 means that the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed, is 0.05.
P = 0.05 does not represent the probability that the null hypothesis is true or false, nor does it signify that the outcome is 5% higher in one group compared to the other. Instead, P = 0.05 is the probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as the one observed. In simpler terms, it indicates the likelihood of obtaining the observed results, or results more extreme, under the assumption that there is no true effect or difference between the groups.
In hypothesis testing, researchers start with a null hypothesis (H0) that states there is no effect or difference between the groups being compared. The alternative hypothesis (Ha), on the other hand, posits that there is a significant effect or difference. The p-value quantifies the strength of evidence against the null hypothesis. A low p-value (such as P = 0.05) suggests that the observed results are unlikely to have occurred by chance alone, leading to the rejection of the null hypothesis in favor of the alternative hypothesis.
When a study reports a statistically significant improvement in Verbal GRE performance with P = 0.05, it means that the probability of obtaining the observed improvement (or a more significant one) under the assumption of no actual effect is 5% or less. Therefore, there is strong evidence to suggest that the technique used in the experiment does indeed have a positive impact on students' Verbal GRE scores.
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Find the height of a square pyramid that has a volume of 25 3/5 meters and a base with 4 meter sides
ANSWER
The height of the square pyramid is 4.8m
EXPLANATION
The volume of a square pyramid is calculated using the formula:
[tex]Volume = \frac{1}{3}(base \: area) \times height[/tex]
It was given that;
The volume of the square pyramid is
[tex]25 \frac{3}{5} {m}^{3} [/tex]
The side length of the square base is
[tex]4m[/tex]
We substitute the given values and then solve for the height.
[tex]25 \frac{3}{5} = \frac{1}{3}( {4}^{2} ) \times height[/tex]
We solve for the height to obtain;
[tex]height = \frac{25 \frac{3}{5} }{ \frac{16}{3} } [/tex]
We simplify to get;
[tex]height = 4.8m[/tex]
Hence, the height of the square pyramid is 4.8 meters.
Answer:
The height of the square pyramid is 4.8 meters.
Step-by-step explanation:
I just know
Consider that the length of rectangle A is 10 cm and its width is 6 cm. Which rectangle is similar to rectangle A? A) A rectangle with a length of 9 cm and a width of 6 cm. B) A rectangle with a length of 15 cm and a width of 9 cm. C) A rectangle with a length of 14 cm and a width of 7 cm. D) A rectangle with a length of 12 cm and a width of 8 cm.
Lata has collected 75 pennies. Lata's father says that if she arranges the pennies in 15 rows, Lata will be able to make a rectangle using all of her pennies. Is her father correct?
Answer:
Yes - he is correct
Step-by-step explanation:
If she has 75 pennies, she would have 15 rows with 5 pennies in each row with a 3:5 ratio for the rectangle.
Lata's father is correct.
What is a rectangle?Rectangle is a type of quadrilateral having two opposite sides that are equal in measurement.All the angles of Rectangle are of 90°.
Area of rectangle = Length * Width
Perimeter of rectangle =2(length + width)
Given,
Total number of pennies Lata have = 75
If she arranges the pennies in 15 rows with 5 pennies in each row.
i.e; 15 * 5 = 75
Then she will get Rectangle of side of length 15 and width 5
So, her father is correct.
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Josh has a rewards card for a movie theater. - He receives 15 points for becoming a rewards card holder. - He earns 3.5 points for each visit to the movie theatre. - He needs at least 55 points to earn a free movie ticket. Which inequality can Josh use to determine x, the minimum number of visits he needs to earn his firs free movie ticket?
A 3.5x+15≥553.5x+15\ge553.5x+15≥55
B 3.5+15x≥553.5+15x\ge553.5+15x≥55
C 3.5+15x ≤ 553.5+15x\ \le\ 553.5+15x ≤ 55
D 3.5x+15 ≤ 553.5x+15\ \le\ 553.5x+15 ≤ 55
Answer:
Option A. 3.5x + 15 ≥ 55
Step-by-step explanation:
Points Rosh received for becoming a member = 15
Points Rosh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
So, option A gives the correct answer
Answer:
option. A
Step-by-step explanation:
I had the exacgt same question