Rodger bowled seven games last week. His scores are: 155, 165, 138, 172, 127, 193, 142. What is the median of Rodger's score?

Step-by-step explanation:

volume of hemisphere (V1)

volume of cylinder (V2)

volume of composite figure =V1+V2

We have the following parameter

Company A

The charges is given by

Company B

The charges is given by

To determine how many miles it will take for the rental cost of company A to exceed B, we will set up the inequality

To find the number of miles, we will make x the subject of the formula

Re-arranging

Therefore, for the rental cost of company A to be better than company B, the number of miles driven in a day must be greater than 600 miles

Answer:

2 out of 5.

Step-by-step explanation:

Answer:

148.3° and 31.7°

Step-by-step explanation:

Supplementary angles add up to 180°

Let x represent the angle we are trying to find

Let y represent the supplementary angle of x

We have x + y = 180  [1]

We are given
x - y = 116.6  [2]

Add both equations. [1] + [2]

x + y + x - y = 180 + 116.6

2x = 296.6

x = 296.6 / 2 = 148.3

y = 180 - 148.3 = 31.7

Therefore the two angles measure 148.3° and 31.7°

Check:
148.3 - 31.7 = 116.6

True. Small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

Small p-values indicate that the observed sample data provides strong evidence against the null hypothesis. The p-value is a measure of the strength of evidence against the null hypothesis in a hypothesis test. It represents the probability of observing the obtained sample data, or more extreme data, if the null hypothesis is true.

When the p-value is small (typically less than a predetermined significance level, such as 0.05), it suggests that the observed sample data is unlikely to have occurred by chance under the assumption of the null hypothesis. In other words, a small p-value indicates that the observed data is inconsistent with the null hypothesis.

Conversely, when the p-value is large (greater than the significance level), it suggests that the observed sample data is likely to occur by chance even if the null hypothesis is true. In such cases, there is not enough evidence to reject the null hypothesis. Therefore, small p-values support the rejection of the null hypothesis and provide evidence in favor of an alternative hypothesis.

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Answer:

The sequence converges to 0.

Step-by-step explanation:

Every new number is divided by 4 and will continue to grow smaller until it converges to 0.

Answer:

BCA = 20 degrees

Step-by-step explanation:

A rhombus is an equilateral quadrilateral, with all four of its sides having the same length. In addition to that, one important geometric property that will really help us with this problem is the fact that the opposite sides of a rhombus are parallel.

This means that BC ||AD.

Consequently, because  BC ||AD,

m∠CAD = m∠BCA.

This is because they are alternate angles.

The alternate angle equality can be used in geometrical problems where you detect two parallel lines cut across by a transversal. in this, our case, the parallel lines BC and AD were transversed by AC.

This makes m∠CAD = m∠BCA because they are alternate angles)

The statements that are true are the volume of the box is v = lwh = 864 in³ and the volume can be expressed in an equation as v = 6x² = 864in³

The volume of a square box is equal to the cube of the length of the side of the square box. The formula for the volume is V = l³, where "l" is the length of the side of the square box.

In the given problem, the volume of the box is 864 cubic inches.

However, we have to remember that the box isn't a square, but rather the base has a square shape.

The volume of the figure is

v = l * w * h

If we divide the volume by the height, we will have the area of the figure

Area = volume / height

Area = 864 / 6

Area = 144 square inches

Since the base has a square shape;

A = l²

144 = l²

l = √144

l = 12 in

The side length is 12 inches.

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Answer:

p = 6/5

Step-by-step explanation:

-4 = 5(p - 2)

-4 = 5p - 10

-4 + 10 = (5p - 10) + 10

6 = 5p

6/5 = (5p)/5

6/5 = p

p = 6/5

Answer:

p = 6/5

Step-by-step explanation:

-4 = 5(p - 2)                       (DISTRIBUTE)

-4 = 5p - 10                        (ADD 10 TO BOTH SIDES)

6 = 5p                                (DIVIDE BY FIVE ON BOTH SIDES)

p = 6/5        

Answer:

b = 20

Step-by-step explanation:

The computation is shown below

Given that

24+ 6b > 138

where

b = 10

b = 15

b = 20

So if we take b = 10

= 24 + 6(10)

= 24 + 60

= 84

B = 15

= 24 + 6(15)

= 24 + 90

= 114

B = 20

= 24 + 6 (20)

= 24 + 120

= 144

So if we take b = 20 the inequality would be true

3x+50

6x-10

6x-10=3x+50

6x-3x=10+50

=3x. 60

(Divide both by 3)

x = 20

Answer:

X= 20 degrees

Step-by-step explanation:

Answer: That is incorrect because the garden will be 17 ft by 17 ft meaning it will be 289 square feet.

Step-by-step explanation:

The product of (3 x 107) and (2 x 107) is 6.8694 x 10^4

To find the product of (3 x 107)and (2 x 107), we can use the distributive property of multiplication which states that the product of a number and a sum is equal to the sum of the products of the number and each term in the sum. In this case, we can multiply the numbers outside the parentheses first, and then multiply the result by the common factor of 107 to simplify the expression:

(3 x 107) x (2 x 107) = 6 x (107 x 107)

Next, we can calculate the product of 107 and 107, which is 11,449:

6 x 11,449 = 68,694

In scientific notation, this can be written as:

= 6.8694 x 10^4

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Answer:

=3x−3

Step-by-step explanation:

=(3)(x+−1)

=(3)(x)+(3)(−1)

Answer:

3x - 3

Step-by-step explanation:

distribution

Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

Answer:

\( \displaystyle ( x_{1},y_{1}) = (0.82, - 3.18) \\ ( x_{2},y_{2}) = ( - 0.82, - 4.82)\)

Step-by-step explanation:

we are given a system of quadratic and linear equation

we want to figure out x and y

in other words the coordinates where the linear function intercept quadrilateral function

to do so

you can use substitution method

since y equals to both equation so substitute:

\( \displaystyle {3x}^{2} + x - 6 = x - 4\)

move right hand side expression to left hand side and change its sign so there's only 0 left on the left hand side:

\( \displaystyle {3x}^{2} + x - 6 - x + 4= 0\)

simplify addition:

\( \displaystyle {3x}^{2} -2=0\)

add 2 to both sides:

\( \displaystyle {3x}^{2} = 2\)

divide both sides by 3

\( \displaystyle \frac{ {3x}^{2} }{3} = \frac{2}{3} \)

\( \displaystyle {x}^{2} = \frac{2}{3} \)

square root both sides:

\( \displaystyle {x} = \sqrt{\frac{2}{3} } \\ x = \frac{ \sqrt{2} }{ \sqrt{3} } \)

rationalise the denominator by multiplying √3/√3:

\( \displaystyle x = \pm\frac{ \sqrt{6} }{3} = \pm0.82\)

now let's figure out y

substitute the value of x to the linear equation:

\(y = \pm0.82 - 4\)

when positive

\(y = - 3.18\)

when negative

\(y = - 4.82\)

Answer:

(x1,y1) = (0.82, - 3.18)

(x2,y2) = (-0.82, -4.82)

Step-by-step explanation:

Plato gang

The image is plotted and attached

The rectangle started with ABCD. Then following the reflection along line AC. point B and point D swapped so we have B' replacing D and D' replacing B.

180 degrees rotation through C, resulted to B'' D'' and A'. Point C maintains it's position since the rotation is about point C.

Enlargement by a factor of 2 results to C' B''' D''' A'' and this is the final image.

While the reflection and rotation preserves the geometry, the enlargement affects the geometry, producing a rectangle with a bigger size twice the initial size

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Usando proporciones, hay que con 200 pesos mx se pueden comprar 0.0645 yenes.

Una proporción es una fracción de la cantidad total, y puede ser encontrada por intermedio de una regla de tres.

En este problema, hay que un yene cuesta $0.17, enquanto $1 = 3100 pesos. Por eso, cada yene es equivalente a 3100 pesos.

Por eso, la regla de tres es:

1 yene - 3100 pesos

x yenes - 200 pesos

Aplicando multiplicación cruzada:

\(3100x = 200\)

\(x = \frac{200}{3100}\)

\(x = 0.0645\)

Con 200 pesos mx se pueden comprar 0.0645 yenes.

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Each function operation should be matched with what it is equivalent to as follows:

f(x) + g(x) = -2x² + x + 6.

g(x) - f(x) = -2x² - 5x + 2.

f(x) · g(x) = -6x³ - 10x² + 8x + 8.

h(x) - f(x) = 3x² - 7x - 2

f(x) · h(x) = 9x³ - 6x² - 8x.

f(x) + g(x) + h(x) = x² - 3x + 6.

In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.

From the information provided, we have the following functions:

f(x) = 3x + 2

g(x) = -2x² - 2x + 4

h(x) = 3x² - 4x

f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)

f(x) + g(x) = 3x + 2 - 2x² - 2x + 4

Next, we would rearrange the function by collecting like terms as follows:

f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)

f(x) + g(x) = -2x² + x + 6 (solution).

g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)

Opening the bracket, we have:

g(x) - f(x) = -2x² - 2x + 4 - 3x - 2

Next, we would rearrange the function by collecting like terms as follows:

g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)

g(x) - f(x) = -2x² - 5x + 2 (solution).

f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)

Opening the bracket, we have:

f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8

Next, we would rearrange the function by collecting like terms as follows:

f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8

f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).

h(x) - f(x) = 3x² - 4x - (3x + 2)

h(x) - f(x) = 3x² - 4x - 3x - 2

h(x) - f(x) = 3x² - 7x - 2 (solution).

f(x) · h(x) = (3x + 2) × (3x² - 4x)

f(x) · h(x) = 9x³ - 12x² + 6x² - 8x

f(x) · h(x) = 9x³ - 6x² - 8x (solution).

f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)

f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x

f(x) + g(x) + h(x) = x² - 3x + 6 (solution).

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Answer:

  7/9

Step-by-step explanation:

You want to evaluate -2x -a for a = 5/9 and x = -2/3.

Put the values of the variables in the corresponding places in the expression and do the arithmetic.

  -2(-2/3) -5/9

  = 4/3 -5/9

  = 12/9 -5/9 = 7/9

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Answer:many

Step-by-step explanation:manymulti- a combining form meaning “many,” “much,” “multiple,” “many times,” “more than one,” “more than two,” “composed of many like parts,” “in many respects,” used in the formation of compound words: multiply; multivitamin.

(a) The 95% confidence interval for proportion of residents in Muscat who consider television news as their major source of news is (0.485, 0.615).

(b) The sample-size of approximately 384 would be necessary to estimate the population proportion with a maximum error of 0.05 at a 95% confidence level.

To construct a confidence-interval for proportion of residents in Muscat who consider television news as their "major-source" of news, we use the  formula;

The Confidence-Interval = Sample Proportion ± Margin of Error

Part (a) : To calculate confidence-interval, we first find the sample proportion (p') and margin-of-error.

The Sample-Proportion (p') = Number of successes / Sample size

p' = 110 / 200 = 0.55,

The Margin-of-Error (ME) = Critical value × Standard Error

The "critical-value" depends on desired confidence-level. For 95% confidence-level, the "critical-value" corresponds to a z-score of 1.96.

The Standard-Error (SE) = √((p' × (1 - p')) / n)

Where n = sample size,

SE = √((0.55 × (1 - 0.55)) / 200) ≈ 0.033

Now we calculate the margin-of-error as :

ME = 1.96 × 0.033 ≈ 0.065,

Now, we construct the confidence interval:

Confidence Interval = 0.55 ± 0.065

Confidence Interval ≈ (0.485, 0.615)

So, the required confidence-interval is (0.485, 0.615).

Part (b) : To determine the sample size required to estimate the population proportion with "maximum-error" of 0.05 at a 95% confidence level, we use the formula:

Sample Size (n) = (Z² × p' × (1 - p'))/E²,

Where Z = critical value corresponding to desired confidence level,

p' = estimated proportion, and E = maximum error,

Using a Z-score of 1.96, and p' = 0.5 and E = 0.05, we calculate the sample size as :

n = (1.96 × 0.5 × (1 - 0.5)) / 0.05²

n ≈ 384.16

Therefore, the required sample-size is 384.

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Answer:

nigrto

Step-by-step explanation:

Answer:

2,457

Step-by-step explanation:

The thousands place is when you move four spaces to the left starting from the first number. In this case, that number was seven, and to round, you need to round it up or down depending if the number to the left of the 4th number is greater or less than 5. In this case, that number was 3, so that 3 and the rest of the remaining numbers turn into 0's, making the rounded number 2,457.

I hope this information was of any use to you.

Answer:

2,457,000

Hope that this helps!

Answer:

2/14, 1/7, 3/21, and 18/126

Step-by-step explanation:

To calculate SAM and SOM, you need to follow the following steps:

1. SAM (Simple Arithmetic Mean): SAM is calculated by adding up all the values in a set of data and then dividing that sum by the number of values in the dataset.

Formula: SAM = (x1 + x2 + ... + xn)/n

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SAM would be (2+4+6+8+10)/5 = 30/5 = 6

2. SOM (Simple Geometric Mean): SOM is calculated by multiplying all the values in a set of data and then taking the nth root of that product, where n is the number of values in the dataset.

Formula: SOM = (x1 * x2 * ... * xn)^(1/n)

Where x1, x2, ..., xn are the values in the dataset and n is the number of values in the dataset.

Example: If you have a dataset with the values 2, 4, 6, 8, 10, then the SOM would be (2*4*6*8*10)^(1/5) = 3840^(1/5) = 5.16

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The correct choice in this case is:

B. The limit does not exist.

A. lim G(x) = (Type an integer or a simplified fraction.) x - 3:

This option asks for the limit of G(x) as x approaches 3 to be expressed as an integer or a simplified fraction. However, since we do not have any specific information about the function G(x) or the graph, it is not possible to determine a numerical value for the limit. Therefore, we cannot fill in the answer box with an integer or fraction. This option is not applicable in this case.

B. The limit does not exist:

If the graph of G(x) shows that the values of G(x) approach different values from the left and right sides as x approaches 3, then the limit does not exist. In other words, if there is a discontinuity or a jump in the graph at x = 3, or if the graph has vertical asymptotes near x = 3, then the limit does not exist.

To determine whether the limit exists or not, we would need to analyze the graph of G(x) near x = 3. If there are different values approached from the left and right sides of x = 3, or if there are any discontinuities or vertical asymptotes, then the limit does not exist.

Without any specific information about the graph or the function G(x), I cannot provide a definite answer regarding the existence or non-existence of the limit.

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Answer:

6 days

Step-by-step explanation:

1050 divided by 175 is 6

Answer:

6

6 times 175 equals 1050

Answer: 9 pizzas

Step-by-step explanation:

From the question, we are informed that Jackson Elementary School ordered 25 pizzas for an awards ceremony and at the end of the day, the principal found 8 1/4 pepperoni pizzas and 7 3/4 sausage pizzas left over.

A reasonable estimate for the number of pizzas the students ate at the awards ceremony will be:

= 25 - (8 1/4 + 7 3/4)

= 25 - 16

= 9 pizzas