32 = q over 2.

I don’t know please help me

Answer:

x=3 and y=

Step-by-step explanation:

Answer:

x=5 and y any number

Step-by-step explanation:

Answer:

$102

Step-by-step explanation:

To find the exact value of the cosecant (csc) of an angle in standard position with a given point on its terminal side, we can use the coordinates of the point to determine the values of the adjacent, opposite, and hypotenuse sides of a right triangle.

In this case, the given point is (-7, 6). To determine the values of the sides, we can use the Pythagorean theorem.

The adjacent side (x-coordinate) is -7.

The opposite side (y-coordinate) is 6.

Using the Pythagorean theorem:

hypotenuse^2 = adjacent^2 + opposite^2

hypotenuse^2 = (-7)^2 + 6^2

hypotenuse^2 = 49 + 36

hypotenuse^2 = 85

Taking the square root of both sides, we get:

hypotenuse = √85

The cosecant (csc) of an angle is the reciprocal of the sine (sin) of that angle. The sine can be determined using the opposite side and the hypotenuse:

sin(theta) = opposite / hypotenuse

sin(theta) = 6 / √85

To find the csc(theta), we take the reciprocal of the sine:

csc(theta) = 1 / sin(theta)

csc(theta) = 1 / (6 / √85)

csc(theta) = √85 / 6

Therefore, the exact value of csc(theta) with a rational denominator is √85 / 6.

The time it will take for your account balance to reach $10,000 is given as follows:

t = 10.8 years.

The balance of an account after t years, using continuous compounding, is given as follows:

A(t) = A(0)e^(kt).

In which:

The parameters for this problem are given as follows:

A(0) = 6500, k = 0.04.

Hence the time needed for a balance of $10,000 is obtained as follows:

10000 = 6500e^(0.04t)

e^(0.04t) = 10000/6500

0.04t = ln(10000/6500) -> ln is the inverse operation of the exponential

t = ln(10000/6500)/0.04

t = 10.8 years.

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Using the general equation for depreciation which is y = A(1 – r)^t, The value of the car in 4 years is $12528.15

The value of the car is solved by using the formula for depreciation which is  y = A(1 – r)t

definition of variables

where

y = current value, = ?

A = original cost, = $24,000

r = rate of depreciation, = 15% and

t = time, in years. = 4 years

substituting the variables

current value, y = A(1 – r)t

current value, y = 24000 * (1 - 0.15)⁴

current value, y = 12528.15

the depreciation is $12528.15

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Answer:

the production line did not pass

Step-by-step explanation:

Step-by-step explanation:

1 - 5 is not equal to 8

2 - 16 is not equal to 8

3 - 12 is equal to 12

4 - 5 is not equal to 17

5 - 0 is not equal to 4

Answer:

20

Step-by-step explanation:

firstly let's find out the side lengths of the triangle using formula

\(length \: = \: \sqrt{(y₂-y1) + ( y₂-y1)}\)

length of AB

\( \sqrt{( - 6 - 2) {}^{2} + ( - 4 - 1) {}^{2} } = \sqrt{89} \)

length of AC

\( \sqrt{( - 6 - 2) {}^{2} + (1 - 1) {}^{2} } = 8\)

length of BC

\( \sqrt{( - 6 - ( - 6)) {}^{2} + (1 - ( - 4)) {}^{2} } = 5\)

Now we have all three side lengths:

a =√89 b = 8 and c = 5

using this formula to find the semi perimeter where a, b and c are the side lengths, input them in

\(s \: = \: \frac{a + b + c}{2} \)

\(s = \frac{ \sqrt{89} + 8 + 5 }{2} = \frac{13 + \sqrt{89} } {2} \)

Use heron's formula

\(area = \sqrt{s(s - a)(s - b)(s - c)} \)

\(area = \sqrt{ \frac{13 + \sqrt{89} }{2}(\frac{13 + \sqrt{89} }{2} - \sqrt{89})( \frac{13 + \sqrt{89} }{2} - 8)(\frac{13 + \sqrt{89} }{2} - 5 } = 20\)

area = 20

Step-by-step explanation:

To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.

Answer:

A

Step-by-step explanation:

lemme meh knw if it was helpful..

The proof of ΔRUV ≅ ΔSUT is shown below.

Given that:

RSTV is a rectangle and U is the midpoint of VT.

Here, We have to Prove:

⇒ ΔRUV ≅ ΔSUT

Now, We can prove as;

Statement                               Reason

1) RSTV is a rectangle               Given

2) Angle V and T are                Because every angle in a rectangle is 90

right triangle.

3) ∠V ≅ ∠T                               Because both are right angle.

4) U is the midpoint of VT.        Given

5) VU = UT                                By midpoint theorem.

6) VR ≅ TS                                Opposite sides of rectangle.

7) ΔRUV ≅ ΔSUT                       By SAS congruency theorem.

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The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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Answer:

Step-by-step explanation:

Lala

Skskskskdkdkd0222222

Answer:

700

Step-by-step explanation:

25 x  28

there is only one property and its multiplication

Answer:

The possible values of k are -0.56, -3.56, -2 and -1.

Step-by-step explanation:

We have the equation of the parabola, .

Substituting x=0, we get that  i.e. y = -1.5k

So, the y-intercept is (0,-1.5k).

Thus, the height of the triangle becomes |-1.5k| = 1.5k

Again, substituting y=0,  i.e.  i.e. x=3 and x=-k

So, the x-intercepts are (3,0) and (-k,0).

Thus, the base of the triangle is 3+k if k>-3 or -3-k if k<-3.

We see that 'k' cannot be 0 or -3 as if k=0, then height = 0, which is not possible. If k= -3, then the base = 0, which is also not possible.

As, area of a triangle = .

Substituting the values, we get,

1.5=

i.e.

i.e. k = -0.56 and k = -3.56

or

1.5=

i.e.

i.e. k = -2 and k = -1.

Thus, the possible values of k are -0.56, -3.56, -2 and -1.

Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       \(0=\frac{1}{3} x-1\)

       \(1=\frac{1}{3} x\)

       \(x=3\)

So x-intercept is the point (3,0).

Based on the height that the wires attach, and the base length of the stakes, the length of the wire is 29 ft.

This can be solved with the Pythagorean theorem because the height can be treated as the height of a right-angled triangle. The base as the base of the triangle.

The length of the wire is the hypothenuse.

Length:
c² = a² + b²

c² = 21² + 20²

c² = 841

c = √841

= 29 ft

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The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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Explanation:

The coordinates are given below as

Concept:

Rule for perpendicularity,

Rule for parallelism

Step 1:

We will calculate the slope of QR using the formula below

By substituting the values, we will have

Step 2:

Calculate the slope of RT using the formula below

By substituting the values, we will have

Hence,

Hence,

The final answer is

Tally won the dirt throwing game and his score was 1.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information, The score of Tally is,

= 3×2 - 3×3 + 4×1.

= 6 - 9 + 4.

= 1.

The score of Awasin is,

= 4×2 - 4×3 + 2×1.

= 8 - 12 + 2.

= - 2.

So, Tally won the game and his score is 1.

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Answer:

c: v=5000(1.35)

Step-by-step explanation:

3.5 interest in point-slope decimal form is 1.35.

v=5000(1.35) is final answer

The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

The function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The coordinate points from the graph are (10, 550) and (30, 200).

Here, slope = (200-550)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 550) in y=mx+c, we get

550=-17.5(10)+c

c=550+175

c=725

So, the equation is y= -17.5x+725

Thus, f(n)= -17.5n+725

a) The fine at every speed should go up by $10.

So, the coordinates are (10, 560) and (30, 210)

New slope (m)= (210-560)(30-10)

= -350/20

= -35/2

= -17.5

Substitute m= -17.5 and (x, y)=(10, 560) in y=mx+c, we get

560=-17.5(10)+c

c=550+175

c=735

So, the equation is y= -17.5x+735

Thus, f(n)= -17.5n+735

b) The fine at every speed should be doubled in construction zones.

So, the coordinates are (20, 550) and (60, 200)

New slope (m)= (200-550)(60-20)

= -350/40

= -8.75

Substitute m= -8.75 and (x, y)=(20, 550) in y=mx+c, we get

550=-8.75(10)+c

c=550+87.5

c=637.5

So, the equation is y= -8.75x+637.5

Thus, f(n)= -8.75n+637.5

Therefore, the function for fine at every speed should be doubled in construction zones is f(n)= -8.75n+637.5.

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Answer: 23 cans of soda/4 people.

or (23/4) cans of soda per person.

Step-by-step explanation:

So we have the rate:

46 cans of soda/ 8 people

First, 46 and 8 are multiples of 2, so we can divide both numerator and denominator by 2:

46/2 = 23

8/2 = 4

Then the rate can be:

23 cans of soda/4 people.

Now 23 is a prime number, so we can not simplify it furthermore

Answer:

Mean, m = 72

Step-by-step explanation:

It is given that, Carl earned grades of 62, 78, 59, and 89 on four math tests.

It is required to find the mean of his grades.

Mean of a data is given by :

\(m=\dfrac{\text{sum of observations}}{\text{total no of observations}}\)

Sum of observations is 62 + 78 + 59 + 89 = 288

Total no of observations are 4

So, mean of his grades is :

\(m=\dfrac{288}{4}\\\\m=72\)

So, the mean of his grades is 72.

Option C is correct. If Carl earned grades of 62, 78, 59, and 89 on four math tests, the mean of his grades is 72

Mean is the average of the given data. It is expressed mathematically as:

\(\overlibe x=\frac{\sum x}{N}\)

\(\sum x\) is the sum of the variables

N is the total test taken

\(\sum x = 62 + 78 + 59 + 89\\\sum x = 288\\\\N = 4\)

Substitute the resulting values into the mean formula:

\(\overline x = \frac{288}{4}\\ \overline x =72\)

This shows that the mean of his grades is 72

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A residual plot is a scatterplot in which the residuals (vertical distances between the predicted and actual values) are plotted against the independent variable. A residual is defined as the difference between the predicted value (based on the regression equation) and the actual value.

Residual plots are a valuable tool for checking the adequacy of the model. It helps us check whether the assumptions of linearity, independence, equal variance, and normality are met or not.

The most basic way to create a residual plot is to plot the residuals against the fitted values. If the points in the residual plot are randomly scattered around the horizontal axis, then the assumption of linearity has been met.

If the points show a pattern, such as a curved line, then the assumption of linearity has been violated.To create a residual plot, follow these steps:

Step 1: Estimate the regression equation and obtain the predicted values (ŷ) and residuals (e). ŷ = b0 + b1X

Step 2: Plot the residuals on the vertical axis and the independent variable (X) on the horizontal axis

.Step 3: Look for patterns in the residual plot. If the points are randomly scattered around the horizontal axis, then the assumptions of linearity, independence, equal variance, and normality are met. If there is a pattern, such as a curved line, then the assumptions have been violated. A residual plot can be used to detect outliers, influential observations, and nonlinearity.

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Answer:

A 90% confidence interval of the true mean is [$119.86, $123.34].

Step-by-step explanation:

We are given that an irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent on textbooks was $121.60.

Also, the standard deviation of the population was $6.36.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                              P.Q.  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\bar X\) = sample mean amount of money spent on textbooks = $121.60

            \(\sigma\) = population standard deviation = $6.36

            n = sample of students = 36

            \(\mu\) = population mean

Here for constructing a 90% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.

So, 95% confidence interval for the population mean, \(\mu\) is ;

P(-1.645 < N(0,1) < 1.645) = 0.90  {As the critical value of z at 5% level

                                                      of significance are -1.645 & 1.645}  

P(-1.645 < \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) < 1.645) = 0.90

P( \(-1.645 \times {\frac{\sigma}{\sqrt{n} } }\) < \({\bar X-\mu}\) < \(1.645 \times {\frac{\sigma}{\sqrt{n} } }\) ) = 0.90

P( \(\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }\) < \(\mu\) < \(\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }\) ) = 0.90

90% confidence interval for \(\mu\) = [ \(\bar X-1.645 \times {\frac{\sigma}{\sqrt{n} } }\) , \(\bar X+1.645 \times {\frac{\sigma}{\sqrt{n} } }\) ]

                                      = [ \(121.60-1.645 \times {\frac{6.36}{\sqrt{36} } }\) , \(121.60+1.645 \times {\frac{6.36}{\sqrt{36} } }\) ]

                                      = [$119.86, $123.34]

Therefore, a 90% confidence interval of the true mean is [$119.86, $123.34].

The lengths of the bases are: 4cm and 12cm.

Since the area of a trapezoid is given by the formula;

Where a and b are the lengths of the bases and h is the height of the trapezoid.

Hence, in this case scenario; it follows that;

a = x = 4cm

b = 3x = 12cm.

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