How to solve? Sara has $100. She gave 3/4 of the money to her sister. She gave 1/2 of the rest of the money to her friend. How much money does she have left after giving the money away?

Answer:

34.7 degrees

Step-by-step explanation:

This is a right triangle trig problem. The angle in question, the angle of elevation, is the base angle that is NOT the right angle. The height of the tree is the side opposite the angle of elevation, and the distance away from the tree is the measure of the base of the right triangle. So the question, then, is "What is the angle that has a ratio equal to the side opposite the angle over the side adjacent to the angle?" This is the definition of the tangent of an angle. The equation will be set up as follows:

[tex]tan\beta =\frac{45}{65}[/tex]

Your calculator needs to be in degree mode when you do this operation. Press 2nd on your calculator then tan and you'll get tan^-1 on your display. This means you are looking for a missing angle. Enter the fraction as 45/65 inside the parenthesis and hit enter and you'll get an angle of 34.69515353. Round to the nearest tenth for 34.7

You will always use the 2nd and sin/cos/tan buttons to find missing angles.

The angle elevation is 34.6 9 degree.

When it lies between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

Given:

Height of tree= 45 foot

Distance= 65 feet

Now, Using Trigonometry

tan [tex]\theta[/tex] = P/ B

        = 45/65

        = 9/ 13

        = 0.6923

[tex]\theta[/tex] = 34.69 degrees.

Hence, the angle elevation is 34.6 9 degree.

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Answer:

2

Step-by-step explanation:

We should put π in place of [tex]\theta[/tex] and 6 in place of [tex]h(\theta)[/tex] in the equation given and then do algebra to find the value of [tex]a[/tex]. Steps are shown below:

[tex]h(\theta)=aSin(\theta-\frac{\pi}{2})+4\\6=aSin(\pi-\frac{\pi}{2})+4\\6=aSin(\frac{\pi}{2})+4\\6=a(1)+4\\6=a+4\\a=6-4\\a=2[/tex]

The answer is 2

Note: the value of [tex]Sin(\frac{\pi}{2})[/tex]  is 1

Answer:

$20,409.79

Step-by-step explanation:

First find John’s quarterly salary. ;$42,000 / 4 = $10,500 ;Total Contributions = John’s + Employer’s ;Total Contributions = $10,500 x 0.05 + $10,500 x 0.03 ;Total Contributions = $840 ;Find the interest rate per compounding period and the number of compounding periods. ;8% / 4 = 2% ;5 x 4 = 20 periods ;The factor from the table for 2% and 20 is 24.29737. ;Amount = $840 x 24.29737 ;Amount = $20,409.79

Answer:

18 racks

Step-by-step explanation:

338/19=17.78 so if you round up you get 18 racks

Ms. Sanchez needs to buy 18 coat racks to accommodate 338 coats, as each rack holds 19 coats and we round up the result of the division 338/19 to the nearest whole number.

The question asks us to determine how many coat racks Ms. Sanchez should buy if she wants to hold 338 coats and each rack holds 19 coats. To find out the number of racks needed, we divide the total number of coats by the number of coats that one rack can hold, which is a straightforward division problem.

We calculate this by dividing 338 (the total number of coats the racks need to hold) by 19 (the number of coats each rack can hold):

338 / 19 = 17.7895...

Since we cannot have a fraction of a coat rack, we round up to the nearest whole number because Ms. Sanchez needs enough racks to hold all the coats, and you cannot purchase a fraction of a rack. Therefore, Ms. Sanchez should buy 18 coat racks to accommodate all 338 coats.

1) The caterpillar was already at 4.5 feet so 4.5 will be added. If it crawls upwards 38 of an inch every minute and the amount of minutes is not specified, this will be represented as 38x. That means the answer is C. f(x) = 38x + 4.5

2) Substitute the known values into the equation. There are 7 people at $8.25 a person, which is a total of $57.75 I used 7 because he invites 6 friends, plus himself. He only has $50 on his gift card, so he won't have enough to cover the cost. The answer is A.

3) They start out with 40lbs and recieve 120 more. They have 160lbs in total. If they sell 8lbs a day for 5 days, thats 8*5 or 40lbs total. 160 - 40 = 120lbs left after 5 days. I'd say the answers are A, B, and D.

4) I think the answer would be C because 1,500 is used to find the number of grams of isotope present after t years. The number of grams can't be 1,500. I hope that makes sense because I'm not sure how to explain it.

5) The growth factor is 2 (2x, x being the number of hours). Multiply by 15 because the lab has 15 of them. The answer is B. f(x) = 15 * 2x

I hope this helps you! I'm sorry if I got any of them wrong!

From the definition of conditional probability:

[tex]P(R_1\mid Q)=\dfrac{P(R_1\cap Q)}{P(Q)}[/tex]

By the law of total probability,

[tex]P(Q)=P(Q\cap R_1)+P(Q\cap R_2)+P(Q\cap R_3)[/tex]

[tex]P(Q)=P(Q\mid R_1)P(R_1)+P(Q\mid R_2)P(R_2)+P(Q\mid R_3)P(R_3)[/tex]

[tex]P(Q)=0.42[/tex]

Since

[tex]P(R_1\cap Q)=P(Q\mid R_1)P(R_1)[/tex]

we end up with

[tex]P(R_1\mid Q)=\dfrac{0.03}{0.42}\approx0.0714[/tex]

Answer:

Step-by-step explanation:

There are 6 letters all together. There 2 letters that if you draw them, you will be successful.

2/6 = 1/3

That means that 1 in 3 times you should draw an A or an E.

Answer:

The area of the base of the cylinder is [tex]14.5\ in^{2}[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

[tex]V=Bh[/tex]

where

B is the area of the base of cylinder

h is the height of the cylinder

In this problem we have

[tex]V=174\ in^{3}[/tex]

[tex]h=12\ in[/tex]

Substitute in the formula  and solve for B

[tex]174=B(12)[/tex]

Apply the division property of equality

[tex]B=174/(12)=14.5\ in^{2}[/tex]

Answer:14.5

Step-by-step explanation: just did it

While 50 miles per hour so 50 multiplied by 4 will give you 200 miles

The second vehicle traveling at 60 miles per hour traveling for 8 hours so multiply 60 x 8 and you will get 480

280 miles farther the second car travels.

Given:

Find:

Solution:

So, as it is given that one car traveled 50 miles per hour for 4 hours that means it travels 50*4 miles = 200 miles.

So, this car travels 200 miles.

Now, the second car traveled 60 miles an hour for 8 hours which means it travels 60*8 miles = 480 miles.

So, the second car travels 480 miles.

Now, for getting how farther the second car traveled we have to subtract the miles traveled by the first car from the second car.

Therefore, second car travels farther = 480 - 200 = 280 miles.

Hence, the second car travels 280 miles farther from the first car.

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Answer:

A.

Line

Step-by-step explanation:

In geometry a straight line is defined as the shortest distance between any two given points. Using the concept of locus, a Line is defined as the locus of all points that are equidistant from two given points.

On the other hand, the locus definition of a circle is the locus of a point that moves at a fixed distance from a center point. This fixed distance is called the radius of the circle.

Final answer:

The correct answer to the student's question is a circle, as it is the locus of all points equidistant from two coinciding points, which are special case foci of an ellipse.

Explanation:

The locus of all points that are the same distance from two given points is called a perpendicular bisector, but this is not one of the options provided. Among the given options, the correct answer is a circle. Thinking geometrically, if the two given points are the foci of an ellipse, the locus of points equidistant to the foci would indeed be a circle, specifically when the foci coincide at the center of the circle. This characteristic relates closely to the definition of an ellipse as provided, which is a closed curve wherein the sum of the distance from the foci to any point on the curve is constant. However, this definition does not fully match the question's condition of being the same distance from the two points, which is a special case of an ellipse where the foci are at the same place, thus forming a circle.

Really hard to make it out, especially the upper limit of the sum, but I think it reads

[tex]\displaystyle\sum_{k=1}^n5k-42[/tex]

(not sure what [tex]n[/tex] is, but that's not very important)

Expand the sum as

[tex]\displaystyle5\sum_{k=1}^nk-42\sum_{k=1}^n1[/tex]

Recall that

[tex]\displaystyle\sum_{k=1}^n1=1+1+\cdots+1=n[/tex]

[tex]\displaystyle\sum_{k=1}^nk=1+2+\cdots+n=\dfrac{n(n+1)}2[/tex]

so that

[tex]\displaystyle\sum_{k=1}^n5k-42=\dfrac{5n(n+1)}2-42n[/tex]

Then just plug in whatever [tex]n[/tex] happens to be.

Answer:

Step-by-step explanation:

[tex]\frac{1}{2}x+\frac{1}{5}y = 2 \mid 5x + 2y = c[/tex]

First let's multiply the 1st equation by 10.

[tex]5x + 2y = 20 \mid 5x + 2y = c[/tex]

So, we can see that the equations have the same coefficients and that implies  they are equal.

So the equation has no solutions for. [tex]c \in R \setminus{20}[/tex]

The given system of linear equations has no solutions only when c is different than 20.

A system of linear equations has no solutions only when both lines are parallel.

Remember that two lines are parallel if the lines have the same slope and different y-intercept.

In this case, our lines are:

(1/2)*x + (1/5)*y = 2

5x + 2y = c

Writing both of these in the slope-intercept form, we get:

y = 5*2 - (5/2)*x

y = c/2 - (5/2)*x

So in fact, in both cases, we have the same slope.

And the only condition to not have any solution is to have:

c/2 ≠ 5*2 = 10

c/2 ≠ 10

c ≠ 10*2 = 20

c ≠ 20

So if c is any value different than 20, the system has no solution.

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Answer:

The answer is : Collision

Step-by-step explanation:

Alex would have to pay collision deductible before he receives a payment from the insurance company.

A deductible is any amount that you have to pay out of pocket when you make a claim.

Collision deductible comes to effect when your vehicle is damaged in an accident. This pays the cost of repairing the vehicle minus the amount of your deductible.

Answer:

FE = 30°

Step-by-step explanation:

arc FGC = arc FG + arc GB + arc BC

220° = 90° + arc GB + 70° . . substitute known values

60° = arc GB . . . . . . . . . . . . . subtract 160°

__

External angle A is half the difference of arcs EG and GB:

30° = (1/2)(arc FE +90° -60°) . . . substitute known values

60° = arc FE + 30° . . . . . . . . . . . multiply by 2 and simplify

30° = arc FE . . . . . . subtract 30°

_____

The key to this problem is the relationship between external angle A and the measures of the arcs it subtends.

Answer:

There is a strong negative relationship between x and y

Step-by-step explanation:

we know that

The correlation coefficient r measures the direction and strength of a linear relationship. It can take a range of values from +1 to -1.

Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship

In this problem

The correlation coefficient for the data is −0.9847

therefore

Is a strong negative correlation

Answer:

D.. Just took . the test

Step-by-step explanation:

For this case we have to define trigonometric relations in a rectangular triangle that the cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.

So, we have:

cos (Θ) = [tex]\frac {9} {15} = \frac {3} {5}[/tex]

Answer:

False

Answer:

The answer, using your equation is: 11 hours, 51 minutes and 44 seconds, that is  the number of daylight hours in that city

Step-by-step explanation:

Ok, in a normal year, the 220th day is the 8 of august, that is 08-08.

So, using x=220, we can estimate the number of daylight hours in that city:

[tex]y=2.15sin(\frac{2\pi }{12}x)+10= 2.15sin(\frac{2\pi }{12}(220))+10[/tex]

Then using a calculator in radians:

[tex]y=2.15(sin(0,524*220))+10[/tex]

[tex]y=2.15(sin(115.192))+10[/tex]

[tex]y=2.15(0,866)+10[/tex]

[tex]y=1.862+10[/tex]

[tex]y=11.862[/tex]

Then, you have that is 11 hours, but what about the 0.862 hours? We convert the to hours knowing that 1 hour has 60 minutes. Then 0,862*60 minutes= 51,72 minutes. And we do this for the 0,72 minutes as well, knowing that 1 minute has 60 seconds, then 0,72*60= 44 seconds.

The number of hours is 11 hours, 51 minutes and 44 seconds

Answer:

D

Step-by-step explanation:

The question is on asymptotes of a hyperbola

General equation for a hyperbola is; (x-h)² /a² - (y-k)²/b² =1

given  y²/36 - x²/121 =1

then h=0 and k=0 thus  Center of hyperbola= (0,0) at the origin.

b²=36,b⇒6   a²=121, a⇒11

Vertices of hyperbola v=( h+a, k) and (h-a, k) = (11,0) and (-11, 0)

Equation of asymptotes is given by;

y=k ± b/a (x-h) and we have found that a=11 and b=6

hence y=0 ± 6/11(x-0)

y=6/11 x and y= -6/11 x

Answer: Option D

[tex]y=\frac{6}{11}x[/tex]

and

[tex]y=-\frac{6}{11}x[/tex]

Step-by-step explanation:

We know that the general equation of a hyperbola with transverse vertical axis has the form:

[tex]\frac{(y-h)^2}{a^2}-\frac{(x-k)^2}{b^2} =1[/tex]

Where the point (h, k) are the coordinates of the center of the ellipse

2b is the length of the transverse horizontal axis

2a is the length of the conjugate axis

The asymptotes are lines to which the hyperbola graphic approaches but never touches.

The asymptotes have the following equation

[tex]y -y_1=\±m(x-x_1)\\\\[/tex]

Where

[tex]m=\frac{a}{b}\\\\y_1 = h\\\\x_1 = k[/tex]

In this case the equation of the ellipse is:

[tex]\frac{y^2}{36} -\frac{x^2}{121}=1[/tex]

Then

[tex]h=y_1= 0\\\\k =x_1= 0[/tex]

[tex]m = \frac{\sqrt{36}}{\sqrt{121}}[/tex]

The asymptotes are:

[tex]y -0=\±\frac{\sqrt{36}}{\sqrt{121}}(x-0)\\\\[/tex]

[tex]y=\±\frac{6}{11}x[/tex]

see the attached image

No, this is not an appropriate question to ask because it doesn't give the person who is taking the survey a variety of options. Also looking at this questionnaire the business will not get the exact answer they want.

if the business wants to have a much more precise feedback on their product then the appropriate question to ask would be.

On a scale of 1 to 10 how much would you rate our product?

This question will give the audience a wider range of answers and they are more likely to give a more honest opinion than if you ask them if they like the product a little or a lot. On the other hand this question will also benefit the company as they can easily find the average of the feedback given.

Final answer:

To find the length of a 90° arc with a circle radius of 10 miles, multiply the radius by π/2. The arc length is calculated to be approximately 15.71 miles.

Explanation:

The radius of a circle is 10 miles, and we're asked to find the length of a 90° arc. The length of an arc can be calculated using the formula arc length = (central angle in radians) × radius. Since there are 2π radians in a 360° circle, a 90° angle corresponds to π/2 radians. Therefore, the arc length for a 90° arc on a circle with a 10-mile radius would be (π/2) × 10 miles.

Calculating the arc length, we get:

arc length = (π/2) × 10 miles

arc length = 5π miles

Using the approximate value of π (3.14159), the arc length would be roughly:

arc length = 5 × 3.14159 miles

arc length = 15.70795 miles

Hence, the length of a 90° arc for a circle with a 10-mile radius is approximately 15.71 miles.

Without further context or diagrams, it's challenging to determine the radii of the stated circles. In general, properties of the equilateral triangle and the relationship between the radius of the circle and the side of the triangle are used in these geometrical problems. More details would permit applying these principles to reach a solution.

Based on the information provided, it appears that there might be some missing context or diagrams for this question. Without further elucidation on Amanda's particular design, it would be difficult to accurately determine the radius of the 'large circle' and the 'smaller circles'.

Generally, in such geometric problems which have circles inside an equilateral triangle, one often uses properties of the equilateral triangle and relations between the radius of the circle and side of the triangle. For instance, in an equilateral triangle, where a circle fits exactly inside the triangle (incircle), the radius could be found by the formula (side of equilateral triangle) / (2*sqrt(3)). Similarly, when a circle is drawn outside the triangle (circumcircle), encompassing it, the radius is calculated as (side of equilateral triangle) / sqrt(3).

However, without additional context or a clear diagram, it's impossible to apply these principles to solve Amanda's challenge.

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Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

21.63

use the Pythagorean theorem.

a^2+b^2=c^2

Answer:

Option c.

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

y=sin^-1 (-1/2x)   on the interval -5 ≤ x ≤ 5

Looking at the graph, we can tell that the correct option is

Option c.

===================================================

Explanation:

Rearrange 0 = x + 2 + x^2 into x^2 + x + 2 = 0

Note that we have something in the form ax^2 + bx + c = 0

where a = 1, b = 1, c = 2

Plug these three values into the discriminant formula

d = b^2 - 4ac

d = 1^2 - 4*1*2

d = 1 - 8

d = -7

The discriminant for the quadratic equation 0 = x squared + x + 2, using the formula b squared - 4ac, and substituting the values a = 1, b = 1 and c = 2, is -7.

The question is asking for the value of the discriminant for the quadratic equation 0 = x2 + x + 2. The discriminant is part of the quadratic formula and its value can be computed using the formula b2 - 4ac. In this equation, a = 1, b = 1, and c = 2. By substituting these values into the formula, we get: (1)2 - 4 * 1 * 2 = 1 - 8 = -7. Therefore, the value of the discriminant for the given equation is -7.

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ANSWER

[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]

EXPLANATION

The given polynomials are:

[tex]G = - 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} [/tex]

and

[tex]P = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} [/tex]

We want to subtract these two polynomials.

[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} - (- 3 {w}^{4} + 2 {w}^{2} {z}^{2} + 5z^{4} )[/tex]

Expand the right hand side to obtain:

[tex]P-G = 8 {w}^{4} - 3{w}^{2} {z}^{2} + z^{4} + 3 {w}^{4} - 2 {w}^{2} {z}^{2} - 5z^{4} [/tex]

Group the similar terms:

[tex]P-G = 8 {w}^{4} + 3 {w}^{4}- 3{w}^{2} {z}^{2} - 2 {w}^{2} {z}^{2} - 5z^{4} + z^{4}[/tex]

Combine the similar terms to get:

[tex]P-G = 11{w}^{4} - 5 {w}^{2} {z}^{2} - 4z^{4}[/tex]

The standard form of the equation of the ellipse is,[tex]\frac{x^2}{7} +\frac{y^2}{14} =1[/tex]. It is obtained by the dividing complete equation by 196.

If the major axis is a units long and the minor axis is b units long, and the ellipse is centered on (0,0). The equation for that ellipse is:

[tex]\rm \frac{x^1}{a^2} +\frac{y^2}{b^2} =1 \\\\\[/tex]

The given equation is;

28x²+14y²=196

Divide the complete equation by 196;

[tex]\rm \frac{28x^2}{196} +\frac{14y^2}{196} =\frac{196}{196} \\\\ \frac{x^2}{7} +\frac{y^2}{14} =1[/tex]

Hence, the standard form of the ellipse is represented as,[tex]\frac{x^2}{7} +\frac{y^2}{14} =1[/tex]

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[tex]\bf \cfrac{5}{\sqrt{30}}\cdot \cfrac{\sqrt{30}}{\sqrt{30}}\implies \cfrac{5\sqrt{30}}{(\sqrt{30})^2}\implies \cfrac{5\sqrt{30}}{30}\implies \cfrac{\sqrt{30}}{6}[/tex]

Answer:

the answer is d

Step-by-step explanation:

Answer:

x = 4.

Step-by-step explanation:

log(x + 6)- log(x - 3) = 1

Using the law log a - log b = log a/b:

log (x + 6)/ (x - 3) = 1

Removing logs:

(x + 6)/ (x - 3) = 10

x+ 6 = 10x - 30

9x = 36

x = 4 (answer).

Answer:

Step-by-step explanation

[tex]log (x+6) - log (x-3) = 1 \\log \frac {x+6}{x-3} = log \ e\\x+6 = e(x-3)\\(1-e)x = -(e+3)\\x=\frac{e+3}{e-1}[/tex]

Step 1: on LHS the difference of two logs, is equal of the log of the division, on RHS, 1 is the log of the base, whatever the base is.

Rest is a 1st grade equation, isolate x, divide.

Answer:

A. 7

Step-by-step explanation:

you bring down the 1 and multiply it by -2 then -2 goes to add with 2, which makes it 0. Then 0 x -2 is 0. 0 then goes to add with -3, then -3 comes down. -2 x -3 is 6. 6+1 is 7.

The remainder in the synthetic division problem is 7.

To find the remainder using synthetic division, follow these steps:

Step 1: Write the coefficients of the polynomial in descending order, including placeholders for missing terms. In this case, the polynomial is given as:

[tex]1x^3 + 2x^2 - 3x + 1[/tex]

Step 2: Since we are dividing by (x + 2), change the sign of the divisor and set it equal to zero to find the value we'll use in the synthetic division.

x + 2 = 0

x = -2

Step 3: Set up the synthetic division table:

       -2  |   1   2   -3   1

Step 4: Perform the synthetic division:

Bring down the first coefficient:         1

Multiply -2 by 1:                             -2

Add the result to the next coefficient:   2 - 2 = 0

Multiply -2 by 0:                              0

Add the result to the next coefficient:   -3 + 0 = -3

Multiply -2 by -3:                            6

Add the result to the next coefficient:   1 + 6 = 7

Step 5: The last entry in the synthetic division row (7 in this case) is the remainder.

The remainder in the synthetic division problem is 7.

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