Consider a triangle ABC like the one below. Suppose that A = 30°, B = 125°, and a = 38. (The figure is not drawn to scale.) Solve the triangle.
Round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".

After simplification, Pierre invested $4000 in the money market account, $92,000 in the stock, and $82000 in the mutual fund.

In the given question we have to find the amount invested in each account.

Suppose, the amount of money invested in the money market account is x, in the stock is y and in the mutual fund is z.

The total amount of money is given as $178,000.

So, the first equation will be:

x+y+z= 178,000.........................(1)

The money in the money market account earns 2.5%(0.025) simple interest, the stock returned 5%(0.05) in the first year and the mutual fund lost 2%(0.02) in the first year. His net gain for 1 year was $3060.

So, the second equation will be:

0.025x+0.05y-0.02z= 3060........................(2)

He invested $10,000 more in the stock than in the mutual fund.

So, the third equation will be:

y= z+10,000...........................(3)

Now substituting equation 3 in equation 1.

x+z+10,000+z= 178,000

x+2z+10,000= 178,000

Subtract 10,000 on both side, we get

x+2z= 178,000-10000

x+2z= 168000

Subtract 2z on both side we get

x = 168000-2z.....................(4)

Now, substituting the equations (3) and (4) into the equation (2),

0.025(168000-2z)+0.05(z+10,000)-0.02z= 3060

Simplifying

0.025*168000-0.025*2z+0.05*z+0.05*10,000-0.02z= 3060

4200-0.05z+0.05z+500-0.02z= 3060

4700-0.02z= 3060

Subtract 4700 on both side

-0.02z = 3060-4700

-0.02z = -1640

Divide by -0.02 on both side, we get

z = 82,000

Put the value of z on equation 4

x = 168000-2*82,000

x = 168,000-164,000

x = 4,000

Now putting the value of z in equation 3

y= 82,000+10,000

y = 92,000

Pierre invested $4000 in the money market account, $92,000 in the stock, and $82000 in the mutual fund.

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Answer:

y= -7

Step-by-step explanation:

Answer:

= 9/8

That's the answer

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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Answer: See below

Step-by-step explanation:

To find the solution of x, we want to use inverse operations to isolate x. The inverse operations are add/subtract and multiply/divide. Be sure to use the corresponding inverse operation.

\(2x^3=28\)                 [divide both sides by 2]

\(x^3=14\)                   [cube root both sides]

\(x=\sqrt[3]{14}\)

I don't see this listed as an answer, but I'm assuming it is meant to be option D.

Answer:

50 degrees

Step-by-step explanation:

Angle ABE is the opposite of the angle given on two converging lines, making it the same degree :)

Answer:

what is your question?

Inequalities help us to compare two unequal expressions. The inequality that model this situation is 1c + 2k ≤ 10. The correct option is C.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

Let c represents the number of carrots and k represents the number of leeks.

Given that At the store, carrots are marked at $1.00 per pound, and leeks are marked at $2.00 per pound. Therefore, the total cost can be written as,

1c + 2k

Also, it is given that Emily wants to buy carrots and leeks for a stew, but she only has $10.00 with her. Therefore, she must spend $10 or less than that.

Thus, the inequality can be written as,

1c + 2k ≤ 10

The graph of the given inequality can be made as shown below.

Hence, the inequality that model this situation is 1c + 2k ≤ 10.

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Answer:

The correct option is c.

Step-by-step explanation:

The percentage probability distribution is:

Size (X)      Percentage

 2                   39.9

 3                   24.4

 4                   20.1

 5                   10.8

 6                    3.3

 7                     1.5

Total             100.0

Compute the probability that the size of the family is 4 or more as follows:

P (X ≥ 4) = P (X = 4) + P (X = 5) + P (X = 6) + P (X = 7)

              = 0.201 + 0.108 + 0.033 + 0.015

              = 0.357

Thus, the probability that the size of the family is 4 or more is 0.357.

The correct option is c.

Answer:

B.

Step-by-step explanation:

Exponential graphs means that it starts to go up slowly but then goes up faster. A is going down, so that's wrong since the graph needs to go up. The correct answer is B.

The y-intercept of the line is y = 2

What is an intercept?

A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.

Here,

A linear function has the following equation:

y = mx + b

Where m is the slope and b is the y-intercept, which is the value of y when x = 0.

We have given three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to construct a system, to find values for m and b.

(-28, -54)

This means that when x = - 28 , y = - 54

so, y = mx + b

- 54 = - 28m + b

28m = b + 54

m = (b + 54)/28

Now, we have x = -21, y = -40

so, y = mx + b

- 40 = - 21m + b

we put the value of m here

- 40 = - 21 {(b + 54)/28} + b  we get,

7b - 1134 = - 40 × 28

b = 2

Hence, the y-intercept of the line is y = 2

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Answer:

(0,2)

Step-by-step explanation:

khan academy

The solution set to the given system of inequalities is represented by the shaded region under the curve of f(x) = x^2 – 3 (including the points on the curve) and above the curve of g(x) = –x^2 + 2 (excluding the points on the curve). The overlapping region between these shaded areas represents the solution set to the system.

To graph the solution set to the system of inequalities y ≤ x^2 – 3 and y > –x^2 + 2, we can modify the graphs of f(x) = x^2 – 3 and g(x) = –x^2 + 2 accordingly. Here's how:

For the inequality y ≤ x^2 – 3:

The original graph of f(x) = x^2 – 3 is an upward-opening parabola with a vertex at (0, -3).

To graph y ≤ x^2 – 3, we need to shade the region below or on the parabola. This includes all points on the parabola itself.

Therefore, we shade the area under the curve of the original graph of f(x) and include the points on the curve.

For the inequality y > –x^2 + 2:

The original graph of g(x) = –x^2 + 2 is a downward-opening parabola with a vertex at (0, 2).

To graph y > –x^2 + 2, we need to shade the region above the parabola. This excludes all points on the parabola itself.

Therefore, we shade the area above the curve of the original graph of g(x) but exclude the points on the curve.

By modifying the graphs of f(x) and g(x) according to these shading instructions, we can graphically represent the solution set to the system of inequalities.

The solution set can be identified by observing the overlapping region or the intersection between the shaded area under the curve of f(x) and the shaded area above the curve of g(x). The points within this overlapping region satisfy both inequalities simultaneously.

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Answer:

y=3x+6

Step-by-step explanation:

the equation of a line in

slope-intercept form

is.

xy=mx+b

The mean absolute deviation (MAD) of the data set is equal to 180.625.

The mean absolute deviation of a data set is to find the average distance of each observation of the data set and the mean of the data set.

Mean absolute deviation = 1/n ∑ absolute value of (xi - x bar)

x bar =average value of the given data set

n= total number of data set

xi = data value in a given set

According to the question,

x bar = sum of all the data set / total number of the data set

x bar = 2052/16 = 128.25

Substitute the value in the formula, we have

Mean absolute deviation = 2890/16 = 180.625

Hence, the Mean absolute deviation of the data set is equal to 180.625.

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As per the given data, the Mean absolute deviation (MAD) of the data set is equals to 17.5

The term Mean absolute deviation in math is defined as the average distance of each observation of data set  and the mean of the data set.

Here we have given the following data.

=> 13, 0 , 14 , 36, 18, 9

Then the mean of the data is calculated as,

=> (13 + 0 + 14 + 36 + 18 + 9)/6

=> 90/6

=> 15

Now, we have to the Substitute the value in the formula, we have

And then the Mean absolute deviation is calculated as,

=> (90 + 15)/6

=> 105/6

=> 17.5

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The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The given values are

x,            f(x)

6,             -2

7,              4

8,              6

9,              4

10,            -2

The equation of the function in vertex form is given as follows;

f(x) = a × (x - h)² + k

To find the values of a, h, and k, we proceed as follows;

When x = 6, f(x) = -2

We have;

-2 = a × (6 - h)² + k = (h²-12·h+36)·a + k.............(1)

When x = 7, f(x) = 4

We have;

4 = a × ( 7- h)² + k = (h²-14·h+49)·a + k...........(2)

When x = 8, f(x) = 6...........(3)

We have;

6 = a × ( 8- h)² + k

When x = 9, f(x) = 4.

We have;

4 = a × ( 9- h)² + k ..........(4)

When x = 10, f(x) = -2...........(5)

We have;

-2 = a × ( 10- h)² + k

Subtract equation (1) from (2)

4-2 =  a × ( 7- h)² + k - (a × (6 - h)² + k ) = 13·a - 2·a·h........(6)

Subtract equation (4) from (2)

a × ( 9- h)² + k - a × ( 7- h)² + k

32a -4ah = 0

4h = 32

h = 32/4

  = 8

From equation (6) we have;

13·a - 2·a·8 = 6

-3a = 6

a = -2

From equation (1), we have;

-2 = -2 × ( 10- 8)² + k

-2 = -8 + k

k = 6

The equation of the function in vertex form is f(x) = -2·(x - 8)² + 6

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Answer:

16 ÷ 8 = 2 16 ÷ 4 = 4 16 × 0 = 0 16 × 2 = 32.

or

16*2=32

Answer:

y = -5x + 7

Step-by-step explanation:

Hi there!

We are given the line y=-5x+4

We want to write an equation of the line that passes through the point (1, 2) and is parallel to y = -5x + 4

Parallel lines have the same slope, so let's first find the slope of y = -5x + 4

The equation is written in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

In this case, -5 is in the place of where m is, so the slope of the line must be -5

It is also the slope of our new line that we are trying to find

As we now know the slope of this line, we can substitute that in as m in y=mx+b

Replace m with -5:

y = -5x + b

Now we need to find b

As the line passes through the point (1, 2), we can use it to help solve for b

Substitute 1 as x and 2 as y.

2 = -5(1) + b

Multiply

2 = -5 + b

Add 5 to both sides

7 = b

Substitute 7 as b into the equation

y = -5x + 7

Hope this helps!

Topic: finding parallel lines

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Answer:

2nd one

as the y is both 4, the points are on the same plane. As such, we care about the distance of x which is between 3 and 7

Answer:

  499.338 feet

Step-by-step explanation:

You want to know the distance traveled by an object in 25 seconds when its velocity is described by 20+5cos(t) feet per second.

The distance an object travels is the integral of its velocity. For the given velocity and time period, the distance is ...

  \(\displaystyle d=\int_0^{25}{v(t)}\,dt=\int_0^{25}{(20+5\cos(t))}\,dt=(20t+5\sin(t))|_0^{25}\\\\d=500+5\sin(25)\approx\boxed{499.338\quad\text{feet}}\)

The distance traveled in 25 seconds is 499.33 feet.

It is required to find the distance traveled in 25 seconds.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

We have to find the distance , we will integrate v(t) from 0 to 25 second.

Consider an object traveling at constant velocity v = k. Then, each second, it travels k feet, so after t seconds, the distance traveled is k*t.

Now, suppose its speed increases by 1 feet/sec . So, estimate for distance traveled after t seconds is

1 + 2 + 3 + 4 + ... + t = t(t+1)/2, or approximately 1/2 t^2.

According to given question we have

Given a velocity function v, the distance s is figured by taking the integral. In this case,

v = 20 + 5 cos(t)

s = 20t + 5 sin(t) from 0 to 25

= s(45)-s(0)

s(0) = 0

so, the distance is

s(25) = 20*25 + 5sin(25)

= 500 -0.661

=499.33 feet.

Therefore, the distance traveled in 25 seconds is 499.33 feet.

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Answer:

D about 44%

Step-by-step explanation:

just took the tests

Using the percentage concept and the given table, it is found that about 39% of males supported Wilson.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

\(P=\frac{a}{b}\times 100%\)

In this problem, males are 46% of the sample, and 18% are males that supported Wilson,

\(P=\frac{18}{46} \times 100=39\)

About 39% of males supported Wilson.

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Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036

The standard exponential function is expressed as:

P(t) = P0e^-rt

Substitute

P(t) = 4001e^-(0.0037)t

If t = 28 (by 2027)

An exponential decay function, and use it to approximate the population in 2027 is P(t) = 4001e^-(0.0037)(28) = P(t) = 4001e^-0.1036

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Answer:

The integer 'A' represents -8.

Answer:

-8

Step-by-step explanation:

Look at the number line, it goes to the left so its negative. It went be back 8 times, so wouldn't it be -8.

Answer:

is there a page we can look at

Step-by-step explanation:

Explanation:

If we replaced y with 3 in choice A, then we get

2y-3 = 6

2(3)-3 = 6

6-3 = 6

3 = 6

which is a false statement. So choice A's solution is not y = 3. We can cross choice A off the list. The same applies with choices B and D as well.

Choice C is the answer because,

11y+4 = 37

11(3)+4 = 37

33+4 = 37

37 = 37

which is true. This confirms choice C.

The domain and range of the graph above in interval notation include the following:

Domain = [-6, 3]

Range = [-3, 3]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-6, 3] or -6 ≤ x < 3.

Range = [-3, 3] or -3 < y < 3

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Answer: The function g(x) represents M(x) = 9 cos (x - #) + 3 after translating I units left and 4 units up.

The translation left I units is represented by subtracting I from x.

The translation up 4 units is represented by adding 4 to the y-coordinate.

So the equation that represents g(x) is:

g(x) = 9 cos (x - #) + 7

Therefore, g(x) = 9 cos (x - #) + 7 is the equation that represents the function g(x) after the translation described in the problem.

Step-by-step explanation: