True or False
Interior Angle - Angle formed by 3 adjacent sides inside the polygon.
Select the appropriate response:

True

False

Answer:

(x-1)(x+6)

Step-by-step explanation:

Answer:

What is the correct factorization of x2 + 5x – 6?

A.) (x – 1) (x + 6)

Complete the factorization shown: 3 then 2 are the blank numbers

Step-by-step explanation:

Answer:

Height of the cone = 4 m

Step-by-step explanation:

Given:

Volume of a cube = (12π) m^3

Radius of the cone = (6/2) m = 3 m

We have to find the value of "x".

And "x" is the height of the cone from the figure shown.

Formula to be used:

Volume of the cone:  1/3(πr^2h)

Here height = "x"

⇒ [tex]V_c_o_n_e=\frac{\pi r^2 h}{3}[/tex]

⇒ [tex]V_c_o_n_e=\frac{\pi r^2 x}{3}[/tex]

⇒ [tex]3\times V_c_o_n_e=\frac{\pi r^2 x}{3}\times 3[/tex]

⇒ [tex]3\times V_c_o_n_e=\pi r^2 x[/tex]

⇒ [tex]\frac{3\times V_c_o_n_e}{\pi r^2} =\frac{\pi r^2\times x}{\pi r^2}[/tex]

⇒ [tex]x=\frac{3\times V_c_o_n_e}{\pi r^2 }[/tex]

⇒ [tex]x=\frac{3\times 12\pi }{\pi (3)^2 }[/tex]

⇒ [tex]x=\frac{36\pi }{9\pi }[/tex]

⇒ [tex]x=\frac{36}{9}[/tex]

⇒ [tex]x=4[/tex] meters.

The height of the cone "x" = 4 meters option A is the right choice.

1. 130 2/3 ft3

2. 226 in.3

3. 33 cm3

4. 4 m

5. 15 m

Answer:

The coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is (6.5, 4)

Step-by-step explanation:

Here we have the points on the line given as

(5, -5)  and  (7, 7)

Therefore to the distance between the x and y coordinates are;

x-coordinate difference,  7 - 5 = 2 and

y-coordinate difference,  7 - (-5) = 12 and

The required ratio is 3:1, that is 3 portions on one side and 1 portion on the other.

Therefore, the total portion of the line is 3 + 1 = 4

So we divide each of the differences between x and y by 3/4 and add it to the coordinate of the first point on the line as follows

x-coordinate difference × 3/4 = 2×3/4 =1.5

y-coordinate difference × 3/4 = 12×3/4 = 9

Therefore, the coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is

x-coordinate = 5 + 1.5 = 6.5

y-coordinate = -5 + 9 = 4

or (6.5, 4).

Answer:

(6.5,4)

Step-by-step explanation:

It looks a little sketchy but its correct

Answer: The test statistic is 1.75.

Step-by-step explanation:

Since we have given that

n = 47

First mean difference = 1

and second mean difference = 1.2

Standard deviation = 0.78

So, the value of test statistic would be

[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{1.2-1}{\dfrac{0.78}{\sqrt{47}}}\\\\t=\dfrac{0.2}{0.114}\\\\t=1.754[/tex]

Hence, the test statistic is 1.75.

The test statistic for the sample showing the difference between reported and actual height, with a mean difference of 1.2 inches, standard deviation of 0.78, and sample size of 47, is 1.96 when rounded to two decimal places.

The test statistic for a sample where the population standard deviation is unknown and the sample size is small can be calculated using a t-test. The formula for the test statistic in a one-sample t-test is t = (\bar{X} - \mu) / (s/\sqrt{n}), where \bar{X} is the sample mean, \mu is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

In this case, we are testing the claim that the mean difference in reported and actual height is greater than 1 inch. The null hypothesis (H0) is that the mean difference is less than or equal to 1 inch, and the alternative hypothesis (H1) is that the mean difference is greater than 1 inch. Given a sample mean difference of 1.2, a sample standard deviation of 0.78, and a sample size of 47, the test statistic is calculated as follows:

t = (1.2 - 1) / (0.78/\sqrt{47})

After calculating and rounding to two decimal places, the test statistic is approximately 1.96

Answer:

C[10] = $18.28

Step-by-step explanation:

Answer:

Area of the shaded region= 80.4 cm²

Step-by-step explanation:

Area of the square = 10×10 cm² = 100cm²

Area of the circle= πr²=π(2.5)²=3.14 ×6.25cm²

= 19.625 cm ²

Area of the shaded region= 100cm²-19.625cm²

= 80.375cm²

Answer:

50

Step-by-step explanation:

divide 20 girls by 2 girls to get 10.

multiply 5 by 10 to get 50 boys.

Answer:

420 meters

Step-by-step explanation:

Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?

Given:

Circumference of circular tire = 2.8 meters

Tire revolves per second = 1.5 times

Question asked:

What is the distance Benjamin travels in 100 seconds?

Solution:

Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.

Now, by unitary method:

In 1 second, tire revolves = 1.5 times

In 100 seconds, tire revolves =  1.5 [tex]\times[/tex] 100

                                                = 150 times

Distance covered by the tire when it revolves 1 time = 2.8 m

Distance covered by the tire when it revolves 150 times = 2.8 [tex]\times[/tex] 150

                                                                                             = 420 meters

Therefore, Benjamin travels 420 meters in 100 seconds.

Answer:

420 meters

Step-by-step explanation:

Q. Benjamin is riding a unicycle. The tire of his unicycle has a circumference of 2.8 m, and the tire revolves 1.5 times per second. What is the distance Benjamin travels in 100 seconds?

Given:

Circumference of circular tire = 2.8 meters

Tire revolves per second = 1.5 times

Question asked:

What is the distance Benjamin travels in 100 seconds?

Solution:

Circumference of circular tire means distance covered by the unicycle's tire when it revolves 1 time that is 2.8 meters.

Now, by unitary method:

In 1 second, tire revolves = 1.5 times

In 100 seconds, tire revolves =  1.5  100

                                               = 150 times

Distance covered by the tire when it revolves 1 time = 2.8 m

Distance covered by the tire when it revolves 150 times = 2.8  150

                                                                                            = 420 meters

Therefore, Benjamin travels 420 meters in 100 seconds.

Final answer:

The area of the semicircle is 0.051 square meters.

Explanation:

The area of a semicircle can be found using the formula A = πr²/2, where r is the radius of the semicircle. In this case, the radius is given as 18 cm. So, substituting this value into the formula, we get A = 3.142 x (18 cm)²/2. Now, let's calculate the area step by step:

Convert the radius to meters: 18 cm = 0.18 m

Square the radius: (0.18 m)² = 0.0324 m²

Multiply by π and divide by 2: 0.0324 m² x 3.142 / 2 = 0.051 m²

Therefore, the area of the semicircle is 0.051 square meters.

Answer:

75/2=32.5

Step-by-Step explanation

15/24 x 100

3/8 x 100

3/4 x 50

3/2 x 25

Answer: D

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 50

x = 32

p = 32/50 = 0.64

q = 1 - 0.64 = 0.36

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.9 = 0.1

α/2 = 0.01/2 = 0.05

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.05 = 0.95

The z score corresponding to the area on the z table is 2.05. Thus, confidence level of 90% is 1.645

Therefore, the 90% confidence interval is

0.64 ± 1.645√(0.64)(0.36)/50

Answer:

no

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Step-by-step explanation:

Given

Now arranging in ascending order

7 , 12 , 13, 24 , 24

No of data (N) = 5

Now

Position of Median

= ( N+1) / 2 th item

= (5+1)/2 th item

= 3rd item

So Now

Exact Median = 13

Answer:

Step 1

Step-by-step explanation:

Trent multiplied one side of the equations by 3 but multiplied the other side of the equation by 1/3.  

Trent should have multiplied both sides of the equation by 3 to isolate g.

Trent's mistake is in step 2 of their solution where they incorrectly multiplied by different values.

Trent's mistake lies in step 2 of their solution. They incorrectly multiplied the numerator and denominator of &frac43 by &frac13. To solve the equation correctly, the numerator and denominator of &frac43 should be multiplied by the same value, which in this case is 3. The correct step would be to multiply &frac43 by 3, resulting in &frac49.

https://brainly.com/question/29050831

#SPJ2

Answer:

Step-by-step explanation:

We start by selecting our pivot column as the most negative value on the bottom row.

This means our pivot column is [tex]x_{1}[/tex]. We now generate a new column by diving our pivot value by our value on the right-most column. This gives us (on a new row)

P/V

12/1 = 12

4/2 = 2

4/1 = 4

We pick our smallest positive value to be our pivot row.

This means our pivot row is our second row, and our pivot column is our first column. We now divide our entire row by our pivot point (our intersection of these two pivots)

This gives us our new second row as

1 3 0 1/2 0 0 2

now we need to eliminate our [tex]x_1[/tex] values from our other rows.

old row 1 - new row 2 gives us new row 1

row two stays the same

old row 3 - new row 2 gives us new now 3.

old row P + 2 new row 2 gives us new row P  

After the first iteration of this algorithm this gives our tableau as: (see attached screenshot)

Answer: A, because the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. So, if the point of the center is [tex](5,7)[/tex] and the radius [tex]2[/tex] , then on the equation should be changed as negative and the radius should be multiplied as [tex]4[/tex], which is [tex](x-5)^2+(y-7)^2=4[/tex]

Answer:

6, 27, 45, 279.

Based on arranging the height of candles in ascending order are:

The correct order of the candles from shortest to tallest would be:

6 in.

27 in.

45 in.

279 in.

Answer:

14

Step-by-step explanation:

she had 22 in all take away 8 then you get 14.

take away 8 because they came from another tree

Answer:

14 peaches

Step-by-step explanation:

10-8=2+12=14

Answer:

C. 5

Step-by-step explanation:

Find the factors of 10 and 35

Factors of 10:

1,2, 5, 10

Factors of 35:

1,5,7, 35

The greatest common factor between both is 5, so C is correct

Answer:in 2 + in a - in b

Step-by-step explanation: edge 2021

The expanded form is ln(2) + ln(a) - ln(b) of the expression  ln(2a/b).

An expression is combination of variables, numbers and operators.

Using the properties of logarithms

log(a/b)=loga-logb

we can expand ln(2a/b) as follows:

ln(2a/b) = ln(2a) - ln(b)

Now we use the property log(ab)=loga+logb

ln(2a) = ln(2) + ln(a)

we can substitute this in the above equation:

ln(2a/b) = ln(2) + ln(a) - ln(b)

Therefore, the expanded form of expression ln(2a/b) is ln(2) + ln(a) - ln(b).

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ7

The population proportion [tex]\( p \)[/tex] is estimated to be between 0.224 and 0.276 based on the given sample data.

To construct a confidence interval estimate for a population proportion [tex]\( p \),[/tex] you can use the following formula:

[tex]\[ \text{Confidence Interval} = \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]

where:

[tex]- \( \hat{p} \)[/tex]is the sample proportion.

[tex]- \( Z \)[/tex] is the Z-score corresponding to the desired confidence level.

[tex]- \( n \)[/tex] is the sample size.

In this case:

[tex]\( n = 840 \)[/tex]

[tex]\( \hat {p} = 0.25 \)[/tex]

The confidence level is not specified, so let's assume a common confidence level of 95%. For a 95% confidence level, the Z-score is approximately 1.96.

Substitute these values into the formula:

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.25(1-0.25)}{840}} \][/tex]

Now, calculate the values:

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.25(0.75)}{840}} \][/tex]

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.1875}{840}} \][/tex]

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \times 0.0132 \][/tex]

Now, compute the upper and lower bounds of the confidence interval:

[tex]\[ \text{Lower Bound} = 0.25 - (1.96 \times 0.0132) \][/tex]

[tex]\[ \text{Upper Bound} = 0.25 + (1.96 \times 0.0132) \][/tex]

Finally, round the values to an appropriate number of decimal places. The confidence interval for the population proportion p  is:

[tex]\[ \text{Confidence Interval} = (0.224, 0.276) \][/tex]

So, with 95% confidence, the population proportion [tex]\( p \)[/tex] is estimated to be between 0.224 and 0.276 based on the given sample data.

To find out the amount of milliliters from liters, multiply the value by 1000. This would give us 1250 mL of soap. Divide this by 50 to figure the amount of money it would take. 25, so multiply that by $0.19, $4.75 per bottle, and then multiply that by two.

Answer: $4.75 for one bottle and $9.50 for both bottles

Answer:

10 Square Inches

Step-by-step explanation:

Trapezoid

Base =12 inches

Height =10 inches

Top side= 10 inches.

Area of a Trapezoid[tex]=\frac{1}{2}(a+b)h, $where a and b are the lengths of the base and top respectively$[/tex]

[tex]=\frac{1}{2}(10+12)*10\\=5*22=110 \:Square\:Inches[/tex]

Area of the Trapezoid=110 Square Inches

Rectangle

Base = 12 inches

Height =10 inches.

Area of a Rectangle=Base X Height

=12 X 10

=120 Square Inches

Difference in Area between the two packages

Difference=Area of Rectangle-Area of Trapezoid

=120-110

=10 Square Inches

Answer:

10 Square Inches

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

please tell me if i am wrong

The domain is the set of all possible input values for the function. In this case, the realistic domain for this situation would be 0 ≤ t ≤ 25, indicating the number of years from the time the motorcycle is purchased up to 25 years later.

The domain of a function in mathematics defines the set of input values for which the function is defined. In this case, the function  [tex]v(t) = 7000 \times 0.91^t[/tex]is used to calculate the value of a motorcycle, where t is the number of years after the motorcycle was bought.

As time can't be negative in this real-world scenario, the smallest value for t is 0, representing the moment the motorcycle is bought. Theoretically, t can be any positive number, although it may not be practical to consider values of t that are too large, because the value of the motorcycle will decrease significantly after several years due to depreciation.

Again, if we assume that the motorcycle will be completely worthless after 25 years, a realistic domain would be 0 ≤ t ≤ 25, that is, from the year the motorcycle is bought to 25 years afterward.

https://brainly.com/question/28599653

#SPJ12

Answer:

The p-value of her test is 0.15386.

Step-by-step explanation:

We are given that a buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten.

She selects a simple random sample of 200 apples from the over 20000 apples on the truck and the sample contains 9 rotten apples.

Let p = proportion of of apples in the shipment that are rotten.

SO, Null Hypothesis, [tex]H_0[/tex] : p = 0.06   {means that the proportion of apples in the shipment that are rotten is equal to 0.06}

Alternate Hypothesis, [tex]H_A[/tex] : p < 0.06   {means that the proportion of apples in the shipment that are rotten is less than 0.06}

The test statistics that will be used here is One-sample z proportion statistics;

                               T.S.  = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of apples that are rotten in a sample of 200 apples = [tex]\frac{9}{200}[/tex]  = 0.045  

           n = sample of apples = 200

So, test statistics  =  [tex]\frac{0.045 -0.06}{{\sqrt{\frac{0.045(1-0.045)}{200} } } } }[/tex]

                              =  -1.02

The value of the test statistics is -1.02.

Now, P-value of the test statistics is given by;

        P-value = P(Z < -1.02) = 1 - P(Z [tex]\leq[/tex] 1.02)

                                            = 1 - 0.84614 = 0.15386

Hence, the p-value of her test is 0.15386.

Using the z-distribution, it is found that the p-value for her test is of 0.1867.

The null hypothesis is:

[tex]H_0: p = 0.06[/tex]

The alternative hypothesis is:

[tex]H_a: p < 0.06[/tex]

The test statistic is given by:

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

In which:

For this problem, the parameters are:

[tex]p = 0.06, n = 200, \overline{p} = \frac{9}{200} = 0.045[/tex]

Hence, the value of the test statistic is:

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

[tex]z = \frac{0.045 - 0.06}{\sqrt{\frac{0.06(0.94)}{200}}}[/tex]

[tex]z = -0.89[/tex]

The p-value is found using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, with z = -0.89, and is of 0.1867.

You can learn more about the use of the z-distribution for an hypothesis test at https://brainly.com/question/25912188

Answer:

A = 9.9648

Step-by-step explanation:

if the triangle is equilateral =>

P = 3L => L = 14.4/3 = 4.8

A = L²√3/4

= (4.8)²√3/4

= 23.04√3/4

= 5.76×1.73

= 9.9648

Answer:

  a:  55°

Step-by-step explanation:

The measure of arc NM is the same as the measure of the central angle that intercepts it: Q. The sum of the central angles of a circle is 360°, so ...

  Q = 360° -120° -60° -65° -60° = 55°

The measure of arc NM is 55°.

Answer:

not able to see the angel

Step-by-step explanation:

Answer:

9/100

Step-by-step explanation:

It would be 9/100 as a fraction if thats what your asking!