Help mee ! Giving 40 pts !!

The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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Answer:

hm

Step-by-step explanation:

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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Ah, simple!

It's important to identify what each part of your equation, which is in slope intercept form.

Let's break it down:

3x = Slope (in this case, it would be \(\frac{3}{1}\), which means to go to the up three units, and right one unit)

-1 = Y-intercept (where your line begins)

If there's any confusion, feel free to leave a comment.

First, expand the terms inside the bracket you will get

\((( \tan {}^{2} (x) + 2 \tan(x) \sin(x) + \sin {}^{2} (x) - ( \tan {}^{2} (x) - 2 \tan(x) + \sin {}^{2} (x) ) {}^{2} = 16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

\(( 4 \tan(x) \sin(x) ) {}^{2} = 16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

\(16 \tan {}^{2} (x) \sin {}^{2} (x) = 16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

\(16 \tan {}^{2} (x) (1 - \cos {}^{2} (x) ) = 16 (\tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

\(16( \tan {}^{2} (x) - \frac{ \sin {}^{2} (x) \cos {}^{2} ( {x}^{} ) }{ \cos {}^{2} (x) } \)

\(16( \tan {}^{2} (x) - \sin {}^{2} (x) ) = 16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

\(16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) = 16( \tan(x) + \sin(x) )( \tan(x) - \sin(x) )\)

h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

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Given:

To solve for j :

Explanation:

Multiplying by 2 on both sides,

Adding 38 on both sides, we get

Final answer:

The value of j is 6.

Raina needs to bike 68 miles on the last day to achieve an average distance of 58 miles per day over the 4-day cross-country biking challenge.

To find the number of miles Raina needs to bike on the last day to achieve an average distance of 58 miles per day over the 4-day cross-country biking challenge, we can use the concept of averages.

Let's denote the number of miles Raina needs to bike on the last day as X.

To find the average, we sum up the total miles biked over the 4 days and divide it by 4:

\(\[ \frac{{47 + 64 + 53 + X}}{4} = 58 \]\)

Now, let's solve for X:

\(\[47 + 64 + 53 + X = 4 \times 58\]\)

164 + X = 232

X = 232 - 164

X = 68

Therefore, Raina needs to bike 68 miles on the last day to achieve an average of 58 miles per day over the 4-day cross-country biking challenge.

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Answer:

Step-by-step explanation:

Answer:

C i think

Step-by-step explanation:

The decay factor of the exponential decay function describing the value of construction equipment is 0.25.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

A percentage is used to represent the degradation rate.

Simply decreasing the percent and dividing it by 100 yields the decimal equivalent.

The decay factor b = 1-r can therefore be calculated.

For instance, the exponential function's decay rate is 0.25, and the decay factor b = 1- 0.25 = 0.75 if the rate of decay is 25%.

So, we know that the depreciation rate is 25%.

Then, the decay rate:

.025

Therefore, the decay factor of the exponential decay function describing the value of construction equipment is 0.25.

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The sound level β in decibels of a sound with an intensity of i is calculated in relation to the threshold of human hearing I₀ by this equation.
β= 10log (I/ I₀)

The threshold of human hearing is 10⁻¹² watts/ meter²

The sound level of a jet plane is approximately 140 db. The intensity of a sound of a jet plane is approximately 100 db.

One tenth of a bel is equivalent to one decibel, which is a relative unit of measurement. It uses a logarithmic scale to express the ratio of two values of a power or root-power quantity. The power ratio of two signals with a one decibel difference in levels is 101/10, or a root-power ratio of 10¹⁄²⁰

A dishwasher or a washing machine can be heard at 70 dB. It makes a fair amount of noise. Noise levels of 70 dB are not regarded as damaging to human hearing. Extended exposure to noise levels exceeding 55-60 dB, however, may be deemed unsettling or irritating.

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The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3

To determine if there is convincing evidence of a difference in the proportions of all teens and young adults who own an iPod or MP3 player, we can perform a hypothesis test.

Let's define the following parameters:

- p₁: Proportion of all teens who own an iPod or MP3 player.

- p₂: Proportion of all young adults who own an iPod or MP3 player.

The null hypothesis (H₀) assumes that there is no difference between the proportions:

H₀: p₁ = p₂

The alternative hypothesis (H₁) assumes that there is a difference between the proportions:

H₁: p₁ ≠ p₂

To test this hypothesis, we can use a two-proportion z-test. We calculate the test statistic using the formula:

z = ((p₁ - p₂) - 0) / √((\(\hat{p}_1\) * (1 - \(\hat{p}_1\)) / n₁) + (\(\hat{p}_2\) * (1 - \(\hat{p}_2\)) / n₂))

Where:

- \(\hat{p}_1\): Sample proportion of teens who own an iPod or MP3 player (79% or 0.79)

- \(\hat{p}_2\): Sample proportion of young adults who own an iPod or MP3 player (67% or 0.67)

- n₁: Sample size of teens (800)

- n₂: Sample size of young adults (400)

Using the given values, we can calculate the test statistic:

z = ((0.79 - 0.67) - 0) / √((0.79 * (1 - 0.79) / 800) + (0.67 * (1 - 0.67) / 400))

Calculating this yields the test statistic z = 5.525.

Next, we can determine the critical value or p-value associated with this test statistic using a significance level (α). Assuming a significance level of 0.05, for a two-tailed test, the critical values are approximately -1.96 and 1.96.

Since the calculated test statistic (5.525) is beyond the critical values of -1.96 and 1.96, we can reject the null hypothesis. There is convincing evidence to suggest that there is a difference in the proportions of all teens and young adults who own an iPod or MP3 player.

In conclusion, the data provide convincing evidence of a difference in the proportions of teens and young adults who own an iPod or MP3 player.

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The appropriate hypotheses for testing the difference in proportions of all teens and young adults who own an iPod or MP3 player are:

Null Hypothesis (H0): The proportion of teens who own an iPod or MP3 player is equal to the proportion of young adults who own an iPod or MP3 player.

Alternative Hypothesis (Ha): The proportion of teens who own an iPod or MP3 player is not equal to the proportion of young adults who own an iPod or MP3 player.

To test if there is a significant difference in the proportions of all teens and young adults who own an iPod or MP3 player, we need to set up appropriate hypotheses. Let's denote the proportion of teens who own an iPod or MP3 player as p1 and the proportion of young adults who own an iPod or MP3 player as p2.

The null hypothesis (H0) assumes that there is no difference between the proportions, so we can state it as:

H0: p1 = p2

The alternative hypothesis (Ha) assumes that there is a difference between the proportions, so we can state it as:

Ha: p1 ≠ p2

Here, p1 represents the true proportion of teens who own an iPod or MP3 player, and p2 represents the true proportion of young adults who own an iPod or MP3 player.

To test these hypotheses, we can use a significance level (α) of 0.05, which is a common choice in hypothesis testing. If the p-value (the probability of observing a test statistic as extreme as the one calculated) is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference in the proportions.

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Answer:

6*5=30= 30/100

Step-by-step explanation:

we will multiply 6* by 5 and after that we will do it fraction by doing that 30/100

Answer:

axis of symetry

Step-by-step explanation:

Beast_Building on yt

Answer:

1/6

Step-by-step explanation:

2/3 of the class has a dog, and 1/4 of the class has a cat. This means that some people will have both a cat and a dog.

You have to find the fraction of students who have both, so you have to multiply 2/3 and 1/4, 2*1 = 2, and 3*4 = 12, so the fraction is 2/12.

2/12 can be simplified to 1/6.

So, the amount of students in the class that have both a cat and a dog are 1/6.

Answer:

The answer is 1/6.

Answer:-

Step-by-step explanation:

-120 - 40- would be -160 because when negative you go up when subtracting.

(not sure if I'm right. take this answer at your own risk)

The water level is rising at a rate of 55/3 ft/min when the water depth is 4 inches. the total area A is 1 ft² + 1 ft² + 2 ft * h = 2 + 2h ft².

Given:

Length of the trough = 10 ft

Width of the top isosceles triangle = 2 ft

Height of the isosceles triangle = 1 ft

Rate of filling water = 11 ft³/min

Desired depth of water = 4 inches = 4/12 ft

Formulae:

Area of an isosceles triangle: A = (1/2) * base * height

Volume of water in the trough: V = ∫(0 to h) A dh

Rate of change of volume: dV/dt = A * (dh/dt)

The cross-sectional area A of the water in the trough consists of two isosceles triangles and a rectangular portion. The area of one isosceles triangle is (1/2) * 2 ft * 1 ft = 1 ft². Thus, the total area A is 1 ft² + 1 ft² + 2 ft * h = 2 + 2h ft².

The volume of water V at depth h is obtained by integrating the area with respect to depth:

V = ∫(0 to h) (2 + 2h) dh = [2h + h²] evaluated from 0 to h = 2h + h² ft³.

To find the rate at which the water level is rising, we differentiate V with respect to time:

dV/dt = d/dt (2h + h²) = 2 * (dh/dt) + 2h * (dh/dt) = 2 * (1/2) ft/min + 2h * (dh/dt) = (dh/dt) + 2h * (dh/dt) = (1 + 2h) * (dh/dt) ft³/min.

Since the rate of filling water is 11 ft³/min, we substitute (dh/dt) = 11 ft³/min into the equation:

dV/dt = (1 + 2h) * (dh/dt) = (1 + 2h) * 11 = 11 + 22h ft³/min.

For a desired depth of 4 inches (h = 4/12 ft), we substitute h = 4/12 into the equation:

dV/dt = 11 + 22 * (4/12) = 11 + 22/3 = 33/3 + 22/3 = 55/3 ft³/min.

Therefore, the water level is rising at a rate of 55/3 ft/min when the water depth is 4 inches.

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The percentage increase in volume required to offset a 10% price reduction when the firm's contribution margin is 30% can be calculated using the following formula:Percentage increase in volume = (Price reduction percentage ÷ Contribution margin percentage) × 100= (10 ÷ 30) × 100= 33.33%

Therefore, there needs to be a 33.33% increase in volume to offset a 10% price reduction when the firm's contribution margin is 30%. A company's contribution margin indicates the portion of each sales dollar that goes towards the company's fixed expenses and profits. To know whether or not a firm will be able to withstand a price reduction, the contribution margin percentage must be considered. The calculation of the percentage increase in volume required to offset a 10% price reduction is done by dividing the price reduction percentage by the contribution margin percentage, and then multiplying by 100. In this particular scenario, a 33.33% increase in volume would be needed to offset a 10% price reduction when the company's contribution margin is 30%.The breakeven level is the level at which the total costs of a company are equal to its total sales. To calculate the percentage contribution margin required to offset a 10% increase in price associated with a 14.3% decrease in volume (the breakeven level), the following formula can be used:Contribution margin percentage = (Price increase percentage ÷ Volume decrease percentage) × 100= (10 ÷ 14.3) × 100= 70.0%Thus, a 70.0% contribution margin percentage would be needed to offset a 10% increase in price associated with a 14.3% decrease in volume (the breakeven level).To offset a 12.5% price reduction in a 60% contribution margin situation, the elasticity can be calculated using the following formula:Elasticity = (Price change percentage ÷ Quantity change percentage) × (1 ÷ Contribution margin percentage)= (12.5 ÷ 12.5) × (1 ÷ 60)= 0.0167Thus, an elasticity of 0.0167 would be needed to offset a 12.5% price reduction in a 60% contribution margin situation.

The percentage increase in volume required to offset a 10% price reduction when the firm's contribution margin is 30% is 33.33%. A 70.0% contribution margin percentage would be needed to offset a 10% increase in price associated with a 14.3% decrease in volume (the breakeven level). An elasticity of 0.0167 would be needed to offset a 12.5% price reduction in a 60% contribution margin situation.

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Answer:

7y+2

Step-by-step explanation:

3y+5y=7y

5-3=2

The size of the quarterly deposits in Shelby's RRSP account was approximately $147.40.

Let's denote the size of the quarterly deposits as \(D\). The total number of deposits made over 9 years is \(9 \times 4 = 36\) since there are 4 quarters in a year. The interest rate per period is \(r = \frac{3.50}{100 \times 12} = 0.0029167\) (3.50% annual rate compounded monthly).

Using the formula for the future value of an ordinary annuity, we can calculate the accumulated value of the RRSP fund:

\[55,000 = D \times \left(\frac{{(1 + r)^{36} - 1}}{r}\right)\]

Simplifying the equation and solving for \(D\), we find:

\[D = \frac{55,000 \times r}{(1 + r)^{36} - 1}\]

Substituting the values into the formula, we get:

\[D = \frac{55,000 \times 0.0029167}{(1 + 0.0029167)^{36} - 1} \approx 147.40\]

Therefore, the size of the quarterly deposits, rounded to the nearest cent, is approximately $147.40.

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To find the equations of the tangent plane and normal line to the surface 2(x − 9)²(y − 5)²(z − 2)² = 10 at the point (10, 7, 4), we first need to find the partial derivatives of the surface at that point:

f_x = 4(x - 9)(y - 5)²(z - 2)²

f_y = 4(x - 9)²(y - 5)(z - 2)²

f_z = 4(x - 9)²(y - 5)²(z - 2)

Evaluating these partial derivatives at (10, 7, 4), we get:

f_x(10, 7, 4) = 4(10 - 9)(7 - 5)²(4 - 2)² = 32

f_y(10, 7, 4) = 4(10 - 9)²(7 - 5)(4 - 2)² = 128

f_z(10, 7, 4) = 4(10 - 9)²(7 - 5)²(4 - 2) = 256

So the equation of the tangent plane at (10, 7, 4) is:

32(x - 10) + 128(y - 7) + 256(z - 4) = 0

Simplifying this equation, we get:

8(x - 10) + 32(y - 7) + 64(z - 4) = 0

The normal vector to the tangent plane is therefore <8, 32, 64>. To find the equation of the normal line, we need a point on the line. Let's take the point (10, 7, 4) on the surface. Then the parametric equations of the normal line are:

x(t) = 10 + 8t

y(t) = 7 + 32t

z(t) = 4 + 64t

So the equation of the normal line is:

(x, y, z) = (10, 7, 4) + t<8, 32, 64>

or

x = 10 + 8t

y = 7 + 32t

z = 4 + 64t

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Answer:

Step-by-step explanation:

d

Answer:

127.253 m^3

Step-by-step explanation:

To find the volume, we start by getting the area of the square base

Mathematically, that will be 4.9^2 m^2

To complete the volume, we multiply the area of the base by the height

= 4.9^2 * 5.3 = 127.253 m^3

Answer:

Step-by-step explanation:

42.4

Answer:

3/26

Step-by-step explanation:

6 of the 52 cards are red

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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We cannot conclude whether the national average is greater than the Washington DC average based on the information provided.

To determine whether the national average ACT score is greater than the Washington DC average, we need to conduct a hypothesis test. However, the question does not provide us with enough information to conduct such a test.

We are given the sample means for both populations, but we do not know the sample sizes, the level of significance, or whether the samples were independent or not. Additionally, we do not have any information on the distribution of the scores, except for the population standard deviation, which may or may not be a reasonable assumption.

Therefore, we cannot make any conclusions about the difference between the national and Washington DC averages without conducting a proper hypothesis test with more information.

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