Help with for review to study for finals next week.

the exact value of sin A  to the nearest ten- thousandth is 0. 6625

a² + b² = c²

The opposite side is unknown, so use the pythagorean theorem to find it

c = hypotenuse = 4

a= opposite site = ?

b= adjacent side = 3

Substitute into the formula

4² = a² + 3²

16 = a² + 9

a² = 16 -9 = 7

Find the square root

a =√7 = 2. 65

To find Sin A, use

Sin A = opposite side ÷ hypotenuse

Sin A = 2. 65 ÷ 4 = 0. 6625

Thus,  the value of sin A is 0. 6625

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The value of df, when x = π/4 and dx = 1/24, is (-5π - 5√2)/(96√2).

To find the derivative of the function f(x) = -5cos(x) + xtan(x), we'll use the sum and product rules of differentiation. Let's start by finding df/dx.

Apply the product rule:

Let u(x) = -5cos(x) and v(x) = xtan(x).

Then, the product rule states that (uv)' = u'v + uv'.

Derivative of u(x):

u'(x) = d/dx[-5cos(x)] = -5 * d/dx[cos(x)] = 5sin(x) [Using the chain rule]

Derivative of v(x):

v'(x) = d/dx[xtan(x)] = x * d/dx[tan(x)] + tan(x) * d/dx[x] [Using the product rule]

= x * sec^2(x) + tan(x) [Using the derivative of tan(x) = sec^2(x)]

Applying the product rule:

(uv)' = (5sin(x))(xtan(x)) + (-5cos(x))(x * sec^2(x) + tan(x))

= 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Simplify the expression:

df/dx = 5xsin(x)tan(x) - 5xcos(x)sec^2(x) - 5cos(x)tan(x)

Now, we need to evaluate df/dx at x = π/4 and dx = 1/24.

Substitute x = π/4 into the derivative expression:

df/dx = 5(π/4)sin(π/4)tan(π/4) - 5(π/4)cos(π/4)sec^2(π/4) - 5cos(π/4)tan(π/4)

Simplify the trigonometric values:

sin(π/4) = cos(π/4) = 1/√2

tan(π/4) = 1

sec(π/4) = √2

Substituting these values:

df/dx = 5(π/4)(1/√2)(1)(1) - 5(π/4)(1/√2)(√2)^2 - 5(1/√2)(1)

Simplifying further:

df/dx = 5(π/4)(1/√2) - 5(π/4)(1/√2)(2) - 5(1/√2)

= (5π/4√2) - (10π/4√2) - (5/√2)

= (5π - 10π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

= (-5π - 5√2)/(4√2)

Now, to evaluate df/dx when dx = 1/24, we'll multiply the derivative by the given value:

df = (-5π - 5√2)/(4√2) * (1/24)

= (-5π - 5√2)/(96√2)

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Answer:

1.5 minutes

Step-by-step explanation:

6 x 1.6 = 9.6

9.6 - 1.5 - 1.3 - 1.5 - 1.7 - 2.1 = 1.5

Answer:

The relationship between the volumes of pyramids and prisms is that when a prism and pyramid have the same base and height, the volume of the pyramid is 1/3 of the volume of the prism.

Hope this helps!! ;)

volume of the prism is three times the volume of the pyramid with the same dimensions.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Volume of a triangular prism = area of base triangle × length of the prism

The volume of a triangular pyramid = (1/3) × Base Area × Height

The relationship between a triangular prism and a triangular pyramid with equal bases and heights is that the volume of the prism is three times the volume of the pyramid.

Therefore, volume of the prism is three times the volume of the pyramid with the same dimensions.

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Divide the population of Utah by the poputlation of Wyoming

Thus, Population of Utah is 5 times the population

Answer:

Step-by-step explanation:

Solution:

We can simplify the ratio 305 : 60 by dividing both terms by the greatest common factor (GCF).

The GCF of 305 and 60 is 5.

Divide both terms by 5.

305 ÷ 5 = 61

60 ÷ 5 = 12

Therefore:

305 : 60 = 61 : 12

The difference of two squares expression is (c) (5x + 3y)(5x - 3y)

The difference of two squares expression is represented as:

a^2 - b^2 = (a + b)(a - b)

Using the above as a guide, we have the following expression in option (c)

(5x + 3y)(5x - 3y)

Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)

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Answer:

The solutions are

x = -1, 1, -2√2, and 2√2.

Step-by-step explanation:

Given the equation

x^4 - 9x² + 8 = 0

Let u = x², then the equation becomes

u² - 9u + 8 = 0

u² - u - 8u + 8 = 0

(u² - u) - (8u - 8u) = 0

u(u - 1) - 8(u - 1) = 0

(u - 8)(u - 1) = 0

u - 8 = 0

=> u = 8

Or

u - 1 = 0

=> u = 1

For u = 8

=> x² = 8

=> x = ±√8 = ±2√2

For u = 1

=> x² = 1

=> x = ±√1 = ± 1

Answer:

B

Step-by-step explanation:

As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.

For a normally distributed data set with a mean of 0 and a standard deviation of 0.5, the proportion of values between -1 and 1 is most closely related to 68%.

Approximately 68% of the data in a normal distribution lies within one standard deviation of the mean, which explains why. One standard deviation below the mean is -0.5, and one standard deviation above the mean is 0.5 since the mean is 0 and the standard deviation is 0.5. As a result, 68% of the data falls into the range of values between -1 and 1, which is one standard deviation from the mean. The closest estimate of the solution is 68%.

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Answer:SOMEONE PLZZZ ANSWER THIS I NEED THE ANSWER TO!!!!!!!!!!!!!!!!!!!!!!!!!!!

Step-by-step explanation:

Answer:

(2+6)+4 = (8)+4 = 12

Step-by-step explanation:

Add the constant of 6 to the constant of 2

2+6

Add the constant 4 to the terms of (2+6)

(2+6)+4

there you go! there's your algebraic expression!

Answer:

The unit rate is 8.

Step-by-step explanation:

(5, 40) = 8

(10, 80) = 8

(15, 120) = 8

you can simply divide and find the unit rate.

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer:

15 $1 bills

10 $5 bills

10 $10 bills

Step-by-step explanation:

Let x = number of $1 bills

"There are five fewer $5-bills than $1-bills."

The number of $5 bills is x - 5

"There are half as many $10-bills as $5-bills."

The number of $10 bills is (x - 5)/2.

A $1 bill is worth $1.

x $1 bills are worth x × 1 = x dollars

A $5 bill is worth $5.

x - 5 $5 are worth 5(x - 5) dollars.

A $10 bill is worth $10.

(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.

Now we add the value of each type of bills and set it equal to $115.

x + 5(x - 5) + 5(x - 5) = 115

x + 10(x - 5) = 115

x + 10x - 50 = 115

11x = 165

x = 15

There are 15 $1 bills.

$5 bills: x - 5 = 10 - 5 = 10

There are 10 $5 bills

$10 bills: (x - 5)/2 = (15 - 5)/2 = 5

There are 5 $10 bills

Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills

Check:

First, we check the total value of the bills.

15 $1 bills are worth $15

10 $5 bills are worth $50

10 $10 bills are worth $50

$15 + $50 + $50 = $115

The total does add up to $115.

Now we check the numbers of bills of each denomination.

The number of $1 is 15.

The number of $5 is 5 fewer that 15, so it is 10.

The number of $10 bills is half the number of $5 bills, so it is 5.

All the given information checks out in the answer. The answer is correct.

Answer: B. 44 ounces

Answer:

what was it ??

Step-by-step explanation:          i taking the test

test test test test test test test test test test

8x²+3y²=24

8x²+3y²-24=0

Let x be 1 ,

Therefore

8+3y²-24=0

3y²-16=0

3y²=16

y²=16/3

y=4/1.7

y=40/17

Take different values of x &y and plot a graph!!!

An ellipse is defined as the path traced by a point as it moves such that the sum of distance from two fixed location is a constant

i) The center of the ellipse, is (0, 0)

ii) The vertex of the ellipse are (-√3, 0), and (√3, 0)

iii) Covertex coordinates are (0, 2·√2), and (0, -2·√2)

iv) Length of the minor axis is 2·√3

v) Length of the major axis is 4·√2

vi) Length of the latus rectum is  \(\underline {\dfrac{3 \cdot \sqrt{2} }{2}}\)

vii) The equation of the directrix, is x = ± 8·√5/5

viii) The equation of the latus rectum = √5

The reason the above values are correct are as follows:

The given equation is presented as follows;

8·x² + 3·y²  = 24

Required:

To find the center, vertex, covertex, length of minor axis, length of latus rectum, equation of directrices and latus rectum

Solution;

i) The general form of the equation of an ellipse is presented as follows;

\(\dfrac{(x- h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1\)

From the given equation, we get;

The center of the

\(\dfrac{8\cdot x^2}{24} + \dfrac{3\cdot y^2}{24} =\dfrac{x^2}{3} + \dfrac{y^2}{8} = 1\)

The equation of the given ellipse, is \(\dfrac{x^2}{3} + \dfrac{y^2}{8} = 1\)

∴ a = √3, b = 2·√2

The value of h, and k, are both 0

Therefore, the center of the ellipse, (h, k) = (0, 0)

ii) The vertex are (h - a, k), and (h + a, k), which gives;

The vertex are (0 - √3, 0), and (0 + √3, 0)

The vertex of the ellipse are (-√3, 0), and (√3, 0)

iii) The coordinates of the covertex of an ellipse are;

(h, k + b), and (h, k - b)

Therefore, the coordinates of the covertex of the given ellipse are;

(0, 0 + 2·√2), and (0, 0 - 2·√2), which gives;

The covertex coordinates = (0, 2·√2), and (0, -2·√2)

iv) The length of the minor axis = 2×a

∴ The length of the minor axis = 2·√3

v) The length of the major axis = 2 × b

∴ The length of the major axis, = 2 × 2·√2 = 4·√2

vi) The length of the latus rectum, LR, is given as follows;

b > a, therefore;

\(LR = \dfrac{2 \cdot a^2}{b}\)

\(LR = \dfrac{2 \times 3}{2 \cdot \sqrt{2} } = \mathbf{ \dfrac{3 \cdot \sqrt{2} }{2}}\)

vii) Equation of directrices

a² = b²·(1 - e²)

3 = 8·(1 - e²)

e² = 1 - 3/8 = 5/8

The equation of the directrix, x = ± a/e

The equation of the directrix, x = ±(2·√2)/√(5/8) = ± 8·√5/5

viii) The focus of the ellipse, C² = 8 - 3 = 5

The equation of the latus rectum = b·e = √8 × √(5/8) = √5

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The equation of a line that passes through points (2,5) and (4,3) is

y = -x+7.

Finding the equation of a line:

First, we need to find out the slope for the given points.

(X1,Y1) = (2,5)

(X2,Y2) = (4,3)

formula for slope(m) = \(\frac{Y2 - Y1}{X2 - X1}\)

substitute the points in the above formula

\(\frac{3 - 5}{4 - 2}\) = \(\frac{-2}{2}\)

\(\frac{-2}{2}\) = -1

slope for the given points(m) = -1.

m = -1

The equation of a line is y-y1 = m(x-x1), where x and y are variables.

substituting the values in the above equation then :

y-5 = -1(x-2)

y-5 = -x+2

y+x = 2+5

x+y = 7

y = -x+7

Therefore, the equation of the line passing through the points (2,5) and (4,3) is y = -x+7

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The correct answer is B. The reduced echelon form of A must have a pivot in each row or there would be more than one possible solution for the equation Ax = b. Therefore, the columns of A must span R3.

For a system of linear equations represented by the matrix equation Ax = b to have a unique solution, the matrix A must have full rank, meaning that the columns of A must span the entire three-dimensional space R3. If the columns of A do not span R3, then there will be more than one solution, which means that the solution is not unique.

In the reduced echelon form of a matrix, each row has a pivot in a unique column. If there is a pivot in every row, this means that the columns of the matrix are linearly independent, which implies that the columns span the entire space. Therefore, in order for the equation Ax = b to have a unique solution, the columns of A must span R3.

The correct answer is B. The reduced echelon form of A must have a pivot in each row or there would be more than one possible solution for the equation Ax = b. Therefore, the columns of A must span R3.

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The depth of the crater in yards is 387.2 yards

Since the crater is 13,937.63 in deep, we convert this to yards.

Since 36 in = 1 yard, we use this conversion factor to convert to yards

13,937.63 in × 1 yard/36 in = 387.16 yards

≅ 387.2 yards to the nearest tenth

So, the depth of the crater in yards is 387.2 yards

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The point slope equation and slope of some lines are given below

1) For y - 6 = 3(x - 5), slope = 3

2) For  y - 4 = -9(x + 8), slope = -9

3) y - 2 = 5x, slope = 5

4) Point slope equation of line whose slope = -10 and passing through   (1, 4)

   y - 4 = -10(x - 1)

5) Point slope equation of line whose slope = 2 and passing through    (5, -3)

      y  + 3 = 2(x - 5)

6) Point slope equation of line whose slope = \(\frac{1}{2}\) and passing through    (-7, -7)

   \(y +7 = \frac{1}{2}(x +7)\\\)

What is equation of line in point slope form?

The most general form of equation of line in point slope form is given by \(y - y_1 = m(x - x_1)\) , \((x_1, y_1)\) is a point on the line

Where m is the slope of the line

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If  \(\theta\) is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = \(tan\theta\)

1) y - 6 = 3(x - 5)

  y - 6 = 3x - 15

  y = 3x - 15 + 6

  y = 3x - 9

  Slope = 3

  If x = 0,

  \(y = 3 \times 0 -9\\y = -9\)

  (0, -9) is a point on the line

2) y - 4 = -9(x + 8)

   y - 4 = -9x - 72

   y = -9x - 72 + 4

   y = -9x - 68

   Slope  = -9

   If x = 0

   \(y = -9 \times 0 -68\\y = -68\)

   (0, -68) is a point on the line

3) y - 2 = 5x

   y = 5x + 2

  Slope = 5

    Putting x = 0

    \(y = 5 \times 0 + 2\\y = 2\)

    (0, 2) is a point on the line

4) Slope = - 10

    The line passes through (1, 4)

    Point slope equation

      y - 4 = -10(x - 1)

5) Slope = 2

    The line passes through (5, -3)

     Point slope equation

      y - (-3) = 2(x - 5)

      y + 3 = 2(x - 5)

6) Slope = \(\frac{1}{2}\)

      The line passes through (5, -3)

     Point slope equation

       \(y - (-7) = \frac{1}{2}(x - (-7))\\y +7 = \frac{1}{2}(x +7)\\\)

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Answer:

See attachment for Venn diagram

Percentage of only TV owners is 16%

Step-by-step explanation:

Given

\(TV\ Owners = 68\%\)

\(Radio\ Owners = 72\%\)

\(None = 12\%\)

Required

Represent with a Venn Diagram

What percentage owned television

From the Venn Diagram and In sets theory; we have that

Total = (TV Owners - Radio and TV Owners) + (Radio Owner - Radio and TV Owners) + Radio and TV Owners + None

Represent Radio and TV Owners with y

\(Total = (TV\ Owners - y) + (Radio\ Owner - y) + y + None\)

Substitute 68% for TV Owners, 72% for Radio Owners, 12& for None:

\(Total = 68\% - y + 72\%- y + y + 12\%\)

Collect Like Terms

\(Total = 68\% + 72\%+ 12\%- y + y - y\)

\(Total = 152\% - y\)

In Sets, Total represents 100%; So, we have

\(100\% = 152\% - y\)

Make y the subject of formula  

\(y = 152\% - 100\%\)

\(y = 52\%\)

The percentage of only TV owners is calculated by subtracting y from TV owners

\(\%P = 68\% - 52\%\)

\(\%P = 16\%\)

Answer:

The answer is 90%

Step-by-step explanation:

The function f(x) is shifted right to get g(x)

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

f(x) = x

g(x) = f(x - 5)

When a number is subtracted from x to get another function, it means that the initial function is shifted to the right by 5 units to get the new function

In this case, it means that f(x) is shifted right to get g(x)

Recall that

f(x) = x

g(x) = f(x - 5)

Also, note that:

The function f(x) is shifted right to get g(x)

if the function f(x) is the blue line, then the graph must be the graph (c)

This is so because the red line is to the right of the blue by 5 units

Also, it means that they have the same slope and the y-intercept of g(x) is -5

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If the relation is represented by the equation y = 2x + 1, the domain would be all real numbers (-infinity, +infinity) and the range would be all real numbers greater than or equal to 1 (1, +infinity).

A relation is a function if for every input (x) there is exactly one output (y). To determine if a relation is a function, we can use the vertical line test, which states that if a vertical line can be drawn through the graph and intersects the relation more than once, then the relation is not a function.

If the relation is a function, we can find the domain and range by analyzing the relation. The domain is the set of all x-values and the range is the set of all y-values. In interval notation, the domain is written as (a, b) and the range is written as (c, d).

So, the domain and range answers depend on the relation which is given and it should be specified.

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Imagine the situation described as a triangle.

They are asking to find the height h, to do this, you can use the sine and the length of the sliding board.

The height of the ladder is 9.6 feet.

Answer:

Solution given:

r=4in

h=4in

surface area=2πr(r+h)=2π*4(4+4)=64π or201.06ft²

Volume=πr²h=π*4²*4=64π or 201.06ft³

Answer:

a) Null hypothesis: \( \mu \geq 863\)

Alternative hypothesis: \( \mu >863\)

b) For this case using the significance level of \(\alpha=0.05\) we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

\( z_{\alpha}=-1.64\)

And the rejection zone would be:

\( z<-1.64\)

c) For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

d) \( p_v = P(z<-2.17) =0.015\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Step-by-step explanation:

Part a

We want to test for this case if the true mean is significantly less than 863 calories so then the system of hypothesis are:

Null hypothesis: \( \mu \geq 863\)

Alternative hypothesis: \( \mu >863\)

Part b

For this case using the significance level of \(\alpha=0.05\) we can use the normal standard distirbution in order to find a quantile who accumulates 0.05 of the area in the left and we got:

\( z_{\alpha}=-1.64\)

And the rejection zone would be:

\( z<-1.64\)

Part c

For this case since the statistic calculated is lower than the critical value we have enough evidence to reject the null hypothesis at 5% of significance

Part d

For this case the p value would be given by:

\( p_v = P(z<-2.17) =0.015\)

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis at the significance level provided

Answer:

A is true

Step-by-step explanation:

PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE

\(\textbf {Allow me to assist you.}\)

\(\textrm {Let's simplify the terms under the radicals.}\)

\(\mathsf {\sqrt{8} - \sqrt{72} + \sqrt{50}}\)

\(\mathsf {\sqrt{2 \times 2^{2}} - \sqrt{2 \times 6^{2}} + \sqrt{2 \times 5^{2}}}\)

\(\mathsf {2\sqrt{2} - 6\sqrt{2} + 5\sqrt{2}}\)

\(\boxed {\sqrt{2}}\)

\(\textbf {The answer is A.}\)