The cash register receipts each day last week at a coffee shop were $1,846, $1,521, $1,439, $1,439, $1,851, $2,722, and $2,540. (a) Find the mean. (Round your answer to to the nearest cent.) ​

The 95% confidence interval for the proportion in the adult population who would say “Yes” of asked is 0.51 and 0.57.

To find the 95% confidence interval for the proportion in the adult population who would say "Yes," we can use the following formula

CI = p ± z × sqrt((p × (1 - p)) / n)

where

p = proportion of the sample who answered "Yes"

z = the z-score corresponding to the desired level of confidence (in this case, 95% corresponds to a z-score of 1.96)

n = sample size

Plugging in the values given in the question, we get

p = 0.54

z = 1.96

n = 1019

CI = 0.54 ± 1.96 × sqrt((0.54 × (1 - 0.54)) / 1019)

CI = 0.54 ± 0.030

CI = (0.51, 0.57)

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I have solved the question in general, as the given question is incomplete,

The complete question is:

Overall, 54% of the sample (550 of 1019 people) answered “Yes.” Find a 95% confidence interval for the proportion in the adult population who would say “Yes” if asked.?

Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer:

EA and EB are equal

Step-by-step explanation:

This is because both of the circles have the same radius AB. The radius is the length from the center of a circle to anywhere on the edge of the circle and is the same no matter where on the circle it is measured from, as long as it goes to the middle. If we focus on just the circle with B at its center, we can see that AB is the radius from the middle to the edge of the circle at A. E also lies on the edge of this same circle, meaning that the length from B to E is that same as AB, the radius. The same logic applies to AE, the length AE is equal to the radius AB because it also runs from the center to the edge of the circle.

Therefore, EA and EB are equal, because they are both radii of two same size circles and are equal to the length of AB.

Hope this helped!

Answer:

k = 16.806404 and k = 95.174404

Step-by-step explanation:

To determine the value of k in which the graph touches, you set both equations equal to each other

4x + k = -x^2 +8x + 20

k = -x^2+4x+20

You can use the quadratic formula -b^2+-(sqrt(b^2-4(a)(c))) / 2a

You will get the values of x = -2.898 and 6.898 for your answers

My bad, I forgot to add also input the values of x in your equation and get k = 16.806404 and k = 95.174404

Answer:

x²+17x+6=xx+17x+6=(17+x)x +6=17+xx+6= 17+x²+6=23+x²

=>x²+17x+6=23+x²

Answer:

v=\(\frac{(w+v)/t}{2}\)

Step-by-step explanation:

just inverse operations and you will always get your answer :)

Answer:20

Step-by-step explanation:

just go on omni

Montraie can make 2 cups of smoothies with the yogurt

From the question, we have the following parameters that can be used in our computation:

Cups of yogurt = 1 1/2

Each smoothie = 3/4 yogurt

Assume there exist a proportional relationship between the cups and the yogurt

The number of smoothies in the yogurt can be calculated using the following equation

Smoothies = (1 1/2)/(3/4)

Evaluate the quotient

Smoothies = 2

Hence, the cups is 2 yogurt

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Answer:The answer is 2 1/6

Step-by-step explanation:

Answer:

24.85 or rounded to 24.9

Step-by-step explanation:

Conversion

K H D____D C M

The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.

Since

By the end of Tina’s bike ride, she traveled a distance of 40 kilometers.

And we know that

1 mile ≈ 1.6 kilometers

So,

\(= 40 \div 1.6\)

= 25 miles

hence, The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.

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Answer:

300 square miles (nearest square mile).

Step-by-step explanation:

Population Density formula

\(\sf Population\;Density=\dfrac{Number\;of\;People}{Land\;Area}\)

Given values:

Substitute the given values into the formula and solve for land area:

\(\implies \sf 29300=\dfrac{8800000}{Land\;Area}\)

\(\implies \sf Land\;Area=\dfrac{8800000}{29300}\)

\(\implies \sf Land\:Area=300.3412969...square\;miles\)

Therefore, the approximate area of New York City is 300 square miles (nearest square mile).

Answer: 300

Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO

Answer:

Hey there!

0.5(8.4)(h)=69.3

4.2h=69.3

h=16.5

Hope this helps :)

Answer:

\( \boxed{\sf Height \ of \ the \ triangle = 16.5 \ mm} \)

Given:

Area of the triangle = 69.3 mm²

Base of the triangle = 8.4 mm

To Find:

Height of the triangle

Step-by-step explanation:

\(\sf \implies Area \ of \ the \ triangle = \frac{1}{2} \times Base \times Height \\ \\ \sf \implies 69.3 = \frac{1}{2} \times 8.4 \times Height \\ \\ \sf \implies 69.3 = \frac{1}{ \cancel{2}} \times \cancel{2} \times 4.2 \times Height \\ \\ \sf \implies 69.3 = 4.2 \times Height \\ \\ \sf \implies 4.2 \times Height = 69.3 \\ \\ \sf \implies Height \times \frac{ \cancel{4.2}}{ \cancel{4.2}} = \frac{69.3}{4.2} \\ \\ \sf \implies Height = \frac{16.5 \times \cancel{4.2}}{ \cancel{4.2}} \\ \\ \sf \implies Height = 16.5 \: mm\)

12 ÷ 5/8

12 x 8/5

(12 • 8)/5

96/5

Done!

Answer:

x=90°

Step-by-step explanation:

As in the angle, there is a box giving us info that x has to be 90°.

But to be sure that there is no mistake we have to do the following:

So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.

The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).

Therefore the answer is:

x=90°

Note that , the simplified expression is (x^2 + 12x + 35)/(7x+35), and x cannot be equal to -5.

First, let's factor the expressions in the numerator and denominator:

(x+7)/(7x+35) = (x+7)/7(x+5)

(x^2 - 3x - 40)/(x-8) = (x-8)(x+5)/(x-8)

Now we can rewrite the original expression as:

[(x+7)/(7(x+5))] * [(x-8)(x+5)/(x-8)]

We can then simplify by canceling out the (x-8) terms in the numerator and denominator:

[(x+7)/(7(x+5))] * [(x+5)]

= (x+7)(x+5)/(7(x+5))

= (x^2 + 12x + 35)/(7x+35)

To find the excluded values, we need to look for values of x that make the denominator equal to zero, since division by zero is undefined. In this case, the excluded value is x = -5 (because it would make the denominator of 7(x+5) equal to zero), so x cannot be equal to -5.

Therefore, the simplified expression is (x^2 + 12x + 35)/(7x+35), and x cannot be equal to -5.

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The difference between the price that DeMarkus thought he should pay and the price that the store charged him is $24

The question provided is incomplete. Here is the complete question : DeMarkus says that a store overcharged him on the price of the video game he bought. He thought the price was marked  1/4 of the original price, but it was really  1/4 off the original price. He misread the advertisement. If the original price of the game was $48 , what is the difference between the price that DeMarkus thought he should pay and the price that the store charged him?  A. $28.50B. $36.00C. $42.50D. $24.00

The first step is to determine the price DeMarkus thought the price of the videogame was = 1/4 of the original price

1/4 x $48 = $12

The second step is to determine the actual discounted price.

Actual discounted price = original price = (1/4 of the price)

48 - (1/4 x $48 = $12)

$48 - $12 = $36

The third step is to determine the difference in the prices

$36 - $12 = $24

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Answer:

{ right angle  } triangle          { angle } to the hypotenuse   sin C =   { y / sin (A)  }   sin A = {sin(C) x }    the hypotenuse if not being used in sin we multiply

Step-by-step explanation:

Answer:

0.75

Step-by-step explanation:

Answer:

$1.33 per ticket cost

Step-by-step explanation:

5 / $3.75 = $1.33 per 1 ticket cost

Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

The variance in the sample data is 220

We are given the following data of 5 salespeople (expressed in thousands of dollars); 40, 60, 65, 70, 80

Suppose that the considered data set is

Then, its standard deviation is the positive square root of the variance of this data set. Variance of data set is the sum of squared differences of the data values from its mean to the total count of data values.

Thus, we get:

\(\sigma = \sqrt{\dfrac{1}{n} \sum_{i=1}^{n} (x_i-\overline{x})^2\)

In the formula above, x represents the mean of the data points, x is the value of an individual data point, and N is the total number of data points.

x = (40+60+65+70+80)/5

x=63

So, the mean of the sample data is 63

Variance =

\(\sigma^2 = \dfrac{\sum_{\forall x_i} (x_i - \overline{x})^2}{n}\)

Therefore, the variance is 220

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We have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

To prove that △ABD ≅ △CBD, we can use the SAS (Side-Angle-Side) congruence criterion.

Given:

∠BDA ≅ ∠BDC (Both are right angles)

D is the midpoint of AC¯¯¯¯¯

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯

BD¯¯¯¯¯ bisects ∠B

Proof:

Since D is the midpoint of AC¯¯¯¯¯, we have AD ≅ CD by the definition of a midpoint.

AB¯¯¯¯¯ ≅ BC¯¯¯¯¯ (Given)

BD¯¯¯¯¯ is a common side for both triangles.

∠BDA ≅ ∠BDC (Given)

To apply the SAS congruence criterion, we need to show that one pair of corresponding sides and the included angle are congruent in both triangles.

AD ≅ CD (Side) - This is true as D is the midpoint of AC¯¯¯¯¯.

∠BDA ≅ ∠BDC (Included Angle) - Both are right angles.

By the SAS congruence criterion, we can conclude that △ABD ≅ △CBD.

Therefore, we have proven that △ABD ≅ △CBD based on the given information and the SAS congruence criterion.

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Answer:

option 4

Step-by-step explanation:

the first movement is a translation and then it is reflected over the y axis

Answer:

A

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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So the perimeter of DEFG is  4√(10), which is approximately 12.65 units if rounded to two decimal places.

Perimeter is a measurement of the total distance around the boundary of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding up the lengths of all the sides of the shape.

Here,

To find the perimeter of DEFG, we need to find the lengths of its sides and add them up. The distance formula can be used to find the length of a line segment between two points in a coordinate plane. The formula is:

d = √((x2 - x1)² + (y2 - y1)²)

Using this formula, we can find the lengths of the sides:

DE = √((3 - 2)² + (4 - 1)²)

= √(10)

EF = √((6 - 3)² + (5 - 4)²)

= √(10)

FG = √((5 - 6)² + (2 - 5)²)

= √(10)

GD = √((2 - 5)² + (1 - 2)²)

= √(10)

Therefore, the perimeter of DEFG is:

DE + EF + FG + GD = √(10) + √(10) + √(10) + √(10)

= 4√(10)

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Answer:

I hope this helps

Step-by-step explanation:

Answer:

The answer to your problem is, D. The range is the best measure of variability, and it equals 32.

Step-by-step explanation:

We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.

The key will equal 2|1 means 21

Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.

Quartile:

Median, Minimum, Maximum, & Range:

Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.

The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .

What is Algebraic expression ?

Algebraic expressions are the concept of expressing numbers the usage of letters or alphabets without specifying their real values. The fundamentals of algebra taught us a way to express an unknown price using letters which includes x, y, z, and so on. these letters are referred to as here as variables. An algebraic expression can be a combination of both variables and constants. Any value this is located earlier than and accelerated with the aid of a variable is a coefficient.

Given

expression ,

4^-3 / 4^-1

= 4 ^ (-3-(-1))

= 4^ (-3+1)

= 4^(-2)

= 1/4^2

= 1/16 .

Therefore , The equivalent expression to the 4^-3 / 4^-1 is 4^-2 or it is also equals to 1/16 .

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Answer:

Null hypothesis (H0): Children with antisocial tendencies have the same difficulty recognizing the emotion of surprise as children without antisocial tendencies. Symbolically: μ = 11.80

Alternative hypothesis (H1): Children with antisocial tendencies have a harder time recognizing the emotion of surprise compared to children without antisocial tendencies. Symbolically: μ > 11.80

The critical region for α = 0.05 with the t distribution would be in the upper tail of the distribution, as this is a one-tailed test (since the alternative hypothesis is directional). The degrees of freedom (df) would need to be determined based on the sample size and specific statistical test being used, but the given information does not provide the value of df.

The estimated standard error would need to be calculated using the given sample size, sample mean, and sample standard deviation. The t statistic would then be calculated as the difference between the sample mean and the hypothesized mean (11.80), divided by the estimated standard error.

Once the t statistic is calculated, it would need to be compared to the critical value of t for the appropriate degrees of freedom and α level (0.05) to determine if it falls in the critical region, and therefore whether the null hypothesis is rejected or not. Based on the given information, the t statistic is not provided, so it is not possible to determine if the null hypothesis should be rejected or not.

Step-by-step explanation: