15x⁴-16x³+0x²+8x-17 ÷ (3x²+x+1)​

Answer: 36

Step-by-step explanation:

6 x 4 = 24 (top box)

(6 x 4) divided by 2 = 12 (bottom triangle)

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer:

22

Step-by-step explanation:

Points Y and X are are the midpoints of the segments HI and HG respectively.

Therefore,

By Mid-segment formula:

IG = 2*YX = 2* 11 = 22 units

Answer:

3. SAS

4. DEB is congruent to CEA

Answer:

B

Step-by-step explanation:

44/77

=0.55

Answer:

x = 12 , y = 60

Step-by-step explanation:

The figure has 2 pairs of parallel sides and is therefore a parallelogram.

The opposite sides and opposite angles are congruent , then

x + 3 = 15 ( subtract 3 from both sides )

x = 12

and y = 60

coreect answer is (a) A minimum of 385 observations are required at the 95% confidence level to estimate the time spent on the phone in the office pool.

What is the required sample size at a 95% confidence level to estimate phone usage in an office pool through work sampling?

we consider the desired confidence level, to determine the required number of observations, estimated proportion, and margin of error. With the supervisor's estimate that 25% of the workers' time is spent on the phone, we use a formula to calculate the sample size. Using a 95% confidence level and the given lower and upper limits, the margin of error is determined as 0.05. Plugging these values into the formula, we find that a minimum of 385 observations are needed to estimate the time spent on the phone with 95% confidence.

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a. 0.9996 which is approximated to 0.4530 is  the probability that at least one of them, b. The mean of X is 1.60, c. the proportion of COVID-19 cases requiring hospitalization is significantly higher than 0.63.

(a) Suppose that a COVID-19 vaccine is 86% effective in preventing the disease when a person is exposed to the virus. If four vaccinated people are exposed to the virus, the probability that at least one of them contracts the disease is 0.4530.

The probability that a vaccinated person does not contract the disease is:1 - 0.86 = 0.14

The probability that all four vaccinated people do not contract the disease is:0.14 x 0.14 x 0.14 x 0.14 = 0.00038

So the probability that at least one of the four vaccinated people contracts the disease is:

1 - 0.00038 = 0.99962P(at least one vaccinated person contracts the disease) = 0.99962P(at least one vaccinated person does not contract the disease)

= 1 - 0.99962 = 0.00038P(at least one of the four vaccinated people contracts the disease) = 1 - P(none of the four vaccinated people contracts the disease)

= 1 - 0.00038 = 0.9996 which is approximated to 0.4530

(b) Suppose that 89% of adults in Ontario have been fully vaccinated against COVID-19 and that 71% of adults in Quebec have been fully vaccinated. A random sample consists of one adult from Ontario and one adult from Quebec. Let X be the number of people in the sample that have been fully vaccinated.

The mean of X is given by :E(X) = np where n is the sample size and p is the probability of success in the population The sample size is 2The probability of success for Ontario is 0.89

The probability of success for Quebec is 0.71

The expected value of X is: E(X) = 2(0.89) + 0(1 - 0.89)(1 - 0.71) = 1.60

The mean of X is 1.60

(c) Suppose that 63% of all COVID-19 cases in people aged 75-80 require hospitalization. During a recent outbreak at a long-term care facility, 13 people aged 75-80 contracted COVID-19 and 10 of those people require hospitalization. To find out whether the number of people requiring hospitalization is significantly high, we need to perform a hypothesis test using the binomial distribution.

Hypotheses:H0: p ≤ 0.63 (The proportion of COVID-19 cases requiring hospitalization is less than or equal to 0.63.)H1: p > 0.63 (The proportion of COVID-19 cases requiring hospitalization is greater than 0.63.)

We will use a significance level of α = 0.05.T

he sample size n is 13.The number of successes (people requiring hospitalization) is 10.The null hypothesis assumes that the proportion of successes is less than or equal to 0.63.

Under this assumption, the mean and standard deviation of the binomial distribution are given by:

μ = np = 13(0.63) = 8.19σ = sqrt(np(1 - p)) = sqrt(13(0.63)(1 - 0.63))

= 1.99

To calculate the z-score, we use the formula: z = (x - μ) / σwhere x is the observed number of successes, μ is the mean, and σ is the standard deviation.

z = (10 - 8.19) / 1.99

= 0.91

The p-value can be found using a standard normal table or calculator. The p-value is the probability of observing a z-score of 0.91 or higher when the null hypothesis is true.

For a one-tailed test at α = 0.05, the critical z-value is 1.645. Since the observed z-score is less than the critical value, we fail to reject the null hypothesis.

There is not enough evidence to conclude that the proportion of COVID-19 cases requiring hospitalization is significantly higher than 0.63.

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Answer:

Step-by-step explanation:

6 faces have an area of 150 cm^2

1 face has an area of 150/6 = 25 cm^2

The formula for the area of one face of a cube = s^2 which is the length of  a side squared.

s^2 = 25

sqrt(s^2) = sqrt(25)

s = 5

1/3

each cat gets 1/3 of the food because 2/3 ÷ 2/1 = 1/3.

The graph that matches sine function y = 2 sin (x – π) + 2 is:

On a coordinate plane, a function has a maximum of 4 and minimum of 0. It completes one period at 2 pi. It decreases through the y-axis at (0, 2).

A graph is a pictorial representation of data. Graphs are usually plotted in a cartesian plane having x and y directions

The graph in the given problem is a graph showing sin function representing sinusoidal waves.

The given equation: y = 2 sin (x – π) + 2

substituting x = 0

y = 2 sin (0 – π) + 2

y = 2 sin (-π ) + 2  (in radians)

y = 2 * 0 + 2

y = 0 + 2

y = 2

Therefore the ordered pair is correct for the graph (0, 2)

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Answer: The answer is D (the last option)

Step-by-step explanation:

The general term of the series is a_n = -5.

What is the general term of the series?

The compute the general term a_n of the series, we first need to find the formula for the individual terms. We know that the partial sum s_n is given by the formula s_n = 5 - 5n. This means that the sum of the first n terms of the series is equal to 5 - 5n.

To find the formula for the general term a_n, we need to look at the difference between consecutive terms in the series. We know that the nth term of the series is equal to the sum of the first n terms minus the sum of the first n-1 terms.

So, we have:

a_n = s_n - s_{n-1}

Substituting the formula for s_n, we get:

a_n = (5 - 5n) - (5 - 5(n-1))

Simplifying, we get:

a_n = -5

Therefore, the general term of the series is a_n = -5.

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The required value of the constant of proportion is 2.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion     —-- 1

Given the relation is y = 2x            —-- 2

On comparing both the equation 1 and 2, we have,

k = 2

Hence, the required value of constant of variation is 2.

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Calculate the square root in both sides of the calculation:

Distribute the square roots

Simplify the square roots.

Then:

Answer:

10 inches

Step-by-step explanation:

┏┓ OK!

┃┣━┓

┛┣━┃

⠀┣━┃

┓┣━┃

┗┻━┛

Answer:

Tariffs

Quotas

Export subsidies

Domestic subsidies

Import licensing

Exchange controls

Financial protectionism

Murky or hidden protectionism

Answer:

y= x + 2

Step-by-step explanation:

The surface area of the rectangular prism figure is S = 838 cm²

Given data ,

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

So, the value of S is given by

The heights of the prism is represented as 7cm.

S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )

On simplifying the equation , we get

S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60

S = 838 cm²

Therefore , the value of S is 838 cm²

Hence , the surface area is S = 838 cm²

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Answer:

To dilate by a scale factor of 2, multiply the length of each side of the shape by 2. If the shape is on a coordinate plane, multiply the coordinates of each vertex of the shape by 2.

Hope it helps

Divide 6.3 meters of leather

between 14

Then

6.3 meters= 630 cm

Now divide

630/14 =

Find m,c,d (max common divisor), between 63 and 14. Its 7.

divide by 7, both numerator and denominator

90/2 = 45

Then answer is , each piece is 45 cm long

Answer:

Below

Step-by-step explanation:

See image attached

We will have the following:

*First: We solve for y:

*Second: We determine two sets of points that belong to the line. In our case we will solve for x = 0 & x = 2. So we would get:

*For x = 0:

So, we would have the point:

*For x = 1:

So, we would have the point:

*Third: We graph:

Step-by-step explanation:

A³B = 4T

A³=4T/B

A = cbrt 4T/B. or

³√(4T/B)

hope this helps.

Answer:

a. Assuming gallons of unleaded regular is denoted by r; and unleaded premium by p.

Revenue from one gallon of unleaded regular is $1.299 and from unleaded premium is $1.379.

Revenue function = 1.299r + 1.379p

b. Cost of one gallon of unleaded regular is $1.219 and for unleaded premium is $1.289.

Cost function = 1.219r + 1.289p

c. Total profit = Revenue - Cost

= 1.299r + 1.379p - 1.219r - 1.289p

= 1.299r - 1.219r + 1.379p - 1.289p

= 0.08p + 0.09p

d. If station sells 100,000 gallons of unleaded regular and 40,000 of unleaded premium;

= (0.08 * 100,000) + (0.09 * 40,000)

= 8,000 + 3,600

= $11,600

Answer:

ans= (2)

Step-by-step explanation:

y=x²-1 is the only quadratic function there

1 is a linear function

3 is a cubic function

4 is a a constant function

Answer:

She was initially at a depth of 24.7 feet before she rose

Step-by-step explanation:

The equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.

To write the equation \(x^2 + y^2 + z^2 = 25\) in spherical coordinates, we need to express x, y, and z in terms of the spherical coordinates (ρ, θ, φ).

In spherical coordinates, ρ represents the distance from the origin to the point, θ represents the azimuthal angle measured from the positive x-axis in the xy-plane, and φ represents the polar angle measured from the positive z-axis.

To transform the Cartesian coordinates (x, y, z) to spherical coordinates, we can use the following equations:

x = ρ sin(φ) cos(θ)

y = ρ sin(φ) sin(θ)

z = ρ cos(φ)

Now let's substitute these equations into the given equation:

\((x^2) + (y^2) + (z^2) = 25\)

(ρ sin(φ) cos(θ))² + (ρ sin(φ) sin(θ))² + (ρ cos(φ))² = 25

ρ² (sin²(φ) cos²(θ) + sin²(φ) sin²(θ) + cos²(φ)) = 25

ρ² (sin²(φ) (cos²(θ) + sin²(θ)) + cos²(φ)) = 25

ρ²(sin²(φ) + cos²(φ)) = 25

ρ²= 25

This simplifies to:

ρ = 5

Therefore, the equation in spherical coordinates is ρ = 5. This equation represents a sphere centered at the origin with a radius of 5 units in the ρ direction.

In spherical coordinates, the equation ρ = 5 describes all points that are at a distance of 5 units from the origin, regardless of the values of θ and φ.

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

range

Step-by-step explanation:

the x values or inputs are called the domain

the y values or outputs are called the range