A cat is stuck on the roof If the ladder is 16 feet long and must be placed six feet long and must be placed six feet away from the building How high can the ladder reach up the building to help save the cat?


14.8 feet


22 feet


37.9 feet


220 feet

The true statement is an exponential function will MULTIPLY the same number each time.

A linear function is represented as:

y = mx + b

An exponential function is represented as:

[tex]y = ab^x[/tex]

The factor [tex]b^x[/tex] means that the number b is multiplied by itself x times

Hence, the word that completes the blank is (a) exponential

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Exponential functions multiply a constant number each time to show growth or decay.

Exponential functions will multiply the same number each time. They model exponential growth or decay where the value increases or decreases at a constant rate over time.

For example, if you multiply 2 by itself multiple times: 2^1, 2^2, 2^3, the result will keep growing exponentially.

In math, exponential functions are denoted as f(x) = a*b^x, where 'b' is the constant multiplied each time for growth or decay.

Answer:

A.Distribute 9, by multiplication, to the variable, a, and to the constant, 8.

B.Write the two multiplications, 9(a) + 9(8)

C.The expression 9(a) is written as 9a.

D.The expression 9(8) equals 72.

F.The equivalent expression is 9a + 72.

Step-by-step explanation:

or rather 9+72

Answer:

7 students

Step-by-step explanation:

Answer:

the answer is 7 people

Step-by-step explanation:

have a great day!

Ahmed's first error was in step 3 where he failed to express 54 in terms of π.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies.

We have,

Diameter = 6 cm

1. Radius = diameter/2

= 6/2

= 3cm

2. Area of base = π × 3²

                          = 9π cm²

3. Multiply the area of the base by the height

= 9π x 6

= 54π cm³

4. Divide 54π by 3 to find the volume of the cone

= 54π/3

= 18π cm³

So, the volume of the cone is 18π cm³.

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Answer: Each gallon costs $3.85

Step-by-step explanation:

We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:

$46.20 ÷ 12 = $3.85

Each gallon costs $3.85

I hope this helps!

Answer:

Each gallon costs $3.85

Step-by-step explanation: We know that Bryan's mom spent $46.20 on gas, and her car can hold up to 12 gallons. Therefore all we have to do is:$46.20 ÷ 12 = $3.85Each gallon costs $3.85I hope this helps!

Answer:

She baked 288 cookies

Step-by-step explanation:

24 X 12 equals 288

Answer:

288 cookies

Step-by-step explanation:

Answer:

The equation is

2y + 85x + 75 = 0

Step-by-step explanation:

Given vertices A(-1,5), B(5,-2) and C(3,5).

Suppose we want to find the median from A

First, we find the midpoint of side BC

Let the midpoint be M = ((x1 + x2)/2, (y1 + y2)/2)

= ((5+3)/2, (-2-5)/2)

= (8/2, -7/2)

= (4, -7/2)

Next, we write the equation of median with A(-1,5) and midpoint M(4,-7/2)

y = mx + c

The slope m = (y2 - y1)/(x2 - x1)

= (-7/2 - 5)/(4 + 1)

= (-17/2)/5

m = -85/2

We find the y-intercept, using A(-1,5)

x = -1, y = 5, m = -85/2

y = mx + c

5 = (-85/2)(-1) + c

c = 5- 85/2

= -75/2

y = -85x/2 - 75/2

Multiply through by 2

2y = -85x - 75

2y + 85x + 75 = 0

And this is the equation

The future value of Michael's investment after 5 years is $44,038.01.

The future value of an annuity can be determined using the following formula:

[tex]FV=PV(1+r/n)^{n}[/tex]

FV = future value

PV = present value

r = annual interest rate

n = number of periods interest held

We can also compute the future value using an online finance calculator as follows:

N (# of periods) = 20 quarters (5 years x 4)

I/Y (Interest per year) = 4%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $2,440.38

Total Interest = $440.38

Thus, the value of Michael's investment after 5 years is $2,440.38.

Answer:

15 dollars

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

We multiply the tip percentage by the amount billed

50% * 30

Change to decimal form

.50 * 30

15

Answer:

Step-by-step explanation:

The measure of center of a group of data is a single central value such as the mean and the median.

The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.

The measure of variability  gives an indication of the spread of the data about the mean. Examples are  the Standard Deviation and the Interquartile Range.

Explaining the difference between a measure of center and a measure of variability.

The measure is an estimate or assesses the extent, quality, value, or effect of (something).

The measure of the center of a group of data is a single central value such as the mean and the median.

The mean is the arithmetical average of the sum of the data and the median is the middle value of the data when placed in ascending sequence.

The measure of variability gives an indication of the spread of the data about the mean. Examples are the Standard Deviation and the Interquartile Range.

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Answer:

800

Step-by-step explanation:

1.35x = 1080 -->

x = 1080/1.35 -->

800

Answer:

[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z>2.739)=0.0616[/tex]  

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.

Step-by-step explanation:

Information provided

[tex]\bar X=42[/tex] represent the sample mean for the assembly time

[tex]s=8[/tex] represent the sample deviation

[tex]n=120[/tex] sample size  

[tex]\mu_o =40[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to conduct a hypothesis in order to see if the true mean is equal to 40 minutes or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu =40[/tex]  

Alternative hypothesis:[tex]\mu \neq 40[/tex]  

The statistic for this case is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]t=\frac{42-40}{\frac{8}{\sqrt{120}}}=2.739[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z>2.739)=0.0616[/tex]  

Since the p value is lower than the significance level of 0.05 we have enough evidence to conclude that the true mean for the assembly time is significantly different from 40 minutes.

The hypothesis testing does not provide sufficient evidence to contradict the supervisor's belief that the job should take 40 minutes on average.

The subject matter refers to the concept of hypothesis testing in statistics, where in context, we are checking whether the actual average assembly time of a kitchen cabinet contradicts the believed assembly time. Hypothesis testing works on a null hypothesis and an alternative hypothesis. In this case, the null hypothesis (H0) can be that the average assembly time equals 40 minutes. The alternative hypothesis (H1) would be that the average assembly time does not equal 40 minutes.

At a 0.05 significance level, we calculate the test statistic (z-score) which represents how many standard deviations a data-point (the sample mean) is from the mean (the supervisor's claimed mean). The z-score is calculated as:

(Sample Mean - Claimed Mean) / (Standard Deviation/ √Number of Observations)

In this case, this becomes: (42-40)/(8/√120) = 1.732. The corresponding p-value for this z-score is 0.083.

Since the p-value is greater than the significance level of 0.05, we cannot reject the null hypothesis. Hence, there isn't overwhelming evidence to contradict the supervisor's belief that the job should take 40 minutes on average.

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Answer:it’s ACD=ECB

Step-by-step explanation:

The correct option is Segment Addition Postulate.

Similarity of triangles. The fundamental theorem of similarity states that a line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Here, we have,

The segment addition postulate states that where there are two points on a line A and C and a third point B can only be located on the line segment AB if and only if the the distances between point A and point B as well as the distance between point B and point C satisfy the equation AB + BC = AC

Therefore, given that in the figure,  the point B is in between point A and point C on segment AC then AB + BC

Similarly, AD = AE + ED.

The correct option is Segment Addition Postulate.

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complete question:

BE || CD 1. Given 2. ∠A ≅ ∠A 2. Reflexive Property 3. ∠ACD ≅ ∠ABE 3. Corresponding angles formed by parallel lines and a transversal are ≅. 4. ∠ADC ≅ ∠AEB 4. Corresponding angles formed by parallel lines and a transversal are ≅. 5. ΔABE ∼ ΔACD 5. AA Similarity Postulate 6. AC AB = AD AE 6. Definition of Similar Triangles 7. AC = AB + BC, AD = AE + ED 7. ??? 8. AB + BC AB = AE + ED AE 8. Substitution 9. AB AB + BC AB = AE AE + ED AE 9. Addition 10. BC AB = ED AE 10. Subtraction Fill in the missing reason for the proof. A) Transitive Property B) Subtraction Property C) SSS Similarity Theorem D) Segment Addition Postulate

Answer:

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.3583 , 0.4579)

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 517

Given data Suppose a sample of 517 suspected criminals is drawn. Of these people, 211 were captured.

'x' =211

The sample proportion

                                   [tex]p^{-} = \frac{x}{n} = \frac{211}{517} =0.4081[/tex]

                                  [tex]q^{-} = 1-p^{-} = 1- 0.4081 = 0.5919[/tex]

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

[tex](p^{-} - Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} )}{n} } , p^{-} + Z_{\frac{\alpha }{2} } \sqrt{\frac{p^{-} (1-p^{-} }{n} } )[/tex]

[tex](0.4081 - 2.326 \sqrt{\frac{0.4081 (0.5919 )}{517} } , 0.4081+ 2.326\sqrt{\frac{0.4081(0.5919 }{517} } )[/tex]

(0.4081-0.0498 , 0.4081 +0.0498)

(0.3583 , 0.4579)

Conclusion:-

98% of confidence intervals for the Population proportion of people who captured after appearing on the 10 most wanted list

(0.3583 , 0.4579)

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 4.9

For the alternative hypothesis,

µ < 4.9

This is a left tailed test.

If the population variance is 0.36, the population standard deviation would be √0.36 = 0.6 psi

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 4.9

x = 4.8

σ = 0.6

n = 210

z = (4.8 - 4.9)/(0.6/√210) = - 2.42

Looking at the normal distribution table, the probability corresponding to the z score is 0.0078

Since alpha, 0.1 > than the p value, 0.0078, then we would reject the null hypothesis. Therefore, there is sufficient evidence at the 0.1 level that the valve performs below the specifications.

Answer: add 4 on both sides

Step-by-step explanation:

Answer:

Isolate the constant

Step-by-step explanation:

i just took it on edge A

Answer:

65 degrees

Step-by-step explanation:

I assume this shape is a triangle. The sum of the three angles in a triangle always equals 180 degrees. So, you add the angles that we have the measurements of and subtract it from 180 to get your answer of 65 degrees. hope this helps:)

Answer:

9.433 miles

Step-by-step explanation:

c^2 = a^2 + b^2

The distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.

The distance between the planes ABC can be found using the Pythagorean theorem since the relationship between the sides AB, BC, and AC forms a right triangle. Given that AB is 5 miles, BC is 8 miles, and AC is the hypotenuse, the distance between the planes ABC can be calculated as follows:

[tex]$$ AC^2 = AB^2 + BC^2 $$[/tex]

Substitute the given values:

[tex]$$ AC^2 = 5^2 + 8^2 $$[/tex]

[tex]$$ AC^2 = 25 + 64 $$[/tex]

[tex]$$ AC^2 = 89 $$[/tex]

Therefore, the distance between the planes ABC is the square root of 89 miles, which is approximately 9.43 miles.

Answer:

[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=48-1=47[/tex]  

And the p value would be:

[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]    

Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week

Step-by-step explanation:

Information given

[tex]\bar X=1.8[/tex] represent the sample mean for the growth

[tex]s=0.5[/tex] represent the sample standard deviation    

[tex]n=48[/tex] sample size    

[tex]\mu_o =2[/tex] represent the value that we want to compare

[tex]\alpha=0.01[/tex] represent the significance level

t would represent the statistic    

[tex]p_v[/tex] represent the p value

System of hypothesis

We need to conduct a hypothesis in order to check if the true mean is less than 2cm per week, the system of hypothesis are :    

Null hypothesis:[tex]\mu \geq 2[/tex]    

Alternative hypothesis:[tex]\mu < 2[/tex]    

Since we don't know the population deviation the statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)    

Replacing the info given we got:

[tex]t=\frac{1.8-2}{\frac{0.5}{\sqrt{48}}}=-2.771[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=48-1=47[/tex]  

And the p value would be:

[tex]p_v =P(t_{(47)}<-2.771)=0.0040[/tex]    

Since the p value is lower than the significance level we have enough evidence to conclude that the true mean for this case for the growth rate is less than 2cm per week

Final answer:

The expression representing the sum of six and the product of three and a variable 'd' is written as 6 + 3d.

Explanation:

The expression that means the sum of six and the product of three and d is written as 6 + 3d.

This expression shows that you first multiply the number three by the variable d, and then add six to the result of that multiplication.

The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), instructs us to perform the multiplication before the addition.

Answer:

(B) Subtract 2/5 from both sides.  

Step-by-step explanation:

What is the best first step in solving Negative 4 x + two-fifths greater-than StartFraction 5 over 10 EndFraction?

(A) Add Two-fifths to both sides.

(B) Subtract Two-fifths from both sides.  <<<<<-------Correct Answer

(C) Multiply both sides by Negative 4 and reverse the inequality symbol.

(D) Divide both sides by 10 and reverse the inequality symbol.

The solution is Option B.

Subtract Two-fifths from both sides and the inequality equation is x < -1/40

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( -4x ) + 2/5 > 5/10

On simplifying the equation , we get

-4x + 2/5 > 1/2

Subtracting 2/5 on both sides of the equation , we get

-4x > ( 1/2 ) - ( 2/5 )

-4x > 1/10

On further simplification , we get

4x < - ( 1/10 )

Divide by 4 on both sides of the equation , we get

x < - ( 1/40 )

Hence , the inequality is x < - ( 1/40 )

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Answer:

Callie's comparison of two options for college education

The true statement is:

She would save $11,300 by choosing option A.

Step-by-step explanation:

Cost Analyses:

Option A:            Community College  + University               Total Expenses

Tuition & Fees    $5,800 ($2,900 x 2) + $19,000 ($9,500 x 2)    = $24,800

Scholarships       ($1,600) ($800 x 2)   + ($20,000) ($10,000 x 2)=($21,600)

Room & Board    $2,500 ($1,250 x 2)  + $23,000 ($11,500 x 2) =   $25,500

Work-Study                                            + ($4,000)  ($2,000 x 2)  = ($4,000)

Total Cost           $6,700                       + $18,000      =                    $24,700

Option B:            4 years' University

Tuition & Fees    $38,000 ($9,500 x 4)

Scholarships       ($40,000) ($10,000 x 4)

Room & Board    $46,000 ($11,500 x 4)

Work-Study         ($8,000)  ($2,000 x 4)

Total Cost          $36,000

Difference between the two options = $11,300 ($36,000 - $24,700

Answer: She would save $11,300 by choosing option A

Step-by-step explanation:

Community College Financial Analysis:

Tuition and fees = 2900

Scholarship and grant = 800

Rooms and board = 1250

University Financial Analysis:

Tuition and fees = 9500

Scholarship and grant = 10000

Rooms and board = 11500

Work study - 2000

Option A :

First two years at college :2 × (2900 + 1250 - 800)

2 × (3350) = $6700

2 years at university : 2 × (9500 +11500 - 2000 - 10000)

2 × 9000 = 18000

Option A total = $(18,000 + 6700) = $24,700

Option B :

4 years at university : 4 × (9500 +11500 - 2000 - 10000)

4 × 9000 = $ 36000

She would be saving $(36,000 - 24,700) = $11,300 by choosing option A

Answer:

The test statistic is [tex]t = -62.5[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} = 0.2*500 = 100[/tex]

The alternate hypotesis is:

[tex]H_{1} < 0.2*500 < 100[/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:

[tex]X = 75, \mu = 100, \sigma = \sqrt{500*0.8*0.2} = 8.94, n = 500[/tex]

So

[tex]t = \frac{75 - 100}{\frac{8.94}{\sqrt{500}}}[/tex]

[tex]t = -62.5[/tex]

The test statistic is [tex]t = -62.5[/tex]

Answer:

[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]  

Step-by-step explanation:

Data given by the problem

n=500 represent the random sample taken

X=75 represent the students in favor to reducing the deficit using only spending cuts

[tex]\hat p=\frac{75}{500}=0.15[/tex] estimated proportion of favor to reducing the deficit using only spending cuts

[tex]p_o=0.2[/tex] is the value that we want to check

z would represent the statistic

System of hypothesis

We want to cehck if the true proportion of students in favor to reducing the deficit using only spending cuts is less than 0.2.:  

Null hypothesis:[tex]p\geq 0.2[/tex]  

Alternative hypothesis:[tex]p < 0.2[/tex]  

The statistic for this case is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing the info provided we got:

[tex]z=\frac{0.15 -0.2}{\sqrt{\frac{0.2(1-0.2)}{500}}}=-2.795[/tex]  

Answer:

− 2( 5 y + 3 ) ( y − 6 )

Step-by-step explanation:

hope it helps

Answer:

I think the answer is 9 3/4, 9.5, 9 3/8, 9.125

Answer:Ella's Procedure And Conclusion are incorrect

Step-by-step explanation:

Answer:

Ellas procedure and conclusion are incorrect

Step-by-step explanation:

Answer:

B)

Step-by-step explanation:

If you try to divide 135 with each number,every number is divisible by 135 XD