Mathematics College

A right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

What are the measures of the angles in triangle ABC?

Answers

Answer 1
Angle C is 90 degrees
Angle B is 16
Angle A is 74
Answer 2

Answer:

90, 74, 16 degrees

Step-by-step explanation:

Given that a right triangle has side lengths AC = 7 inches, BC = 24 inches, and AB = 25 inches.

We find that

AC square + BC square = AC square

[tex]7^2 +24^2 =625 = 25^2[/tex]

So angle C = 90 degrees.

sin A = 24/25

So A = 74 degrees and B = 16 degrees

Related Questions

The formula for finding the circumference of a circle is C=2πrC=2πr . Rearrange the formula to solve for the radius (r).

Answers

C=2πr

Divide by 2π:

r = C/2π

Valerie predicts she will be able to hold her breath for 31 second while underwater. If she actually held her breath for 34 seconds, what was Valerie's percent error? Round your answer to the nearest tenth of a percent.

Answers

(predicted value - exact value)/exact value * 100
(31 - 34)/34 * 100 = 8.8%

If she actually held her breath for 34 seconds. Then the percentage error will be 8.82%.

What is the percentage error?

The amount of error is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Valerie predicts she will be able to hold her breath for 31 seconds while underwater.

If she actually held her breath for 34 seconds.

Then the percentage error will be

[tex]\rm error \ \% = \dfrac{34-31}{34} \times 100\\\\\\error \ \% = \dfrac{3}{34} \times 100\\\\\\error \ \% = 8.82 \%[/tex]

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Jason deposits $5,000 in a bank account that will pay him 4% simple interest annually. If Jason deposits no more than the initial 5,000 , how much money will be in the account at the end of 5 years ?

Answers

F=I(1+rt), F=final amount, I=initial amount, r=rate, t=time

Here I=$5000, r=(4/100)=0.04 so

F=$5000(1+0.04t)  so after 5 years...

F=$5000(1+0.2)

F=$6000

In a recent local taste contest testing Coke against Pepsi it was found that 3/5 of all people surveyed preferred to taste the Coke. if 7,500 people were in the survey how many chose Pepsi ?

Answers

3/5 of 7500 is 4500. That means 4500 chose coke. Now all u need to do is subtract 4500 from 7500 to get the amount of people that chose Pepsi. The answer would be 3000

Answer: 3,000

Step-by-step explanation:

Given : In a recent local taste contest testing Coke against Pepsi it was found that [tex]\dfrac{3}{5}[/tex] of all people surveyed preferred to taste the Coke.

If 7,500 people were in the survey , then the number of people chose coke will be :-

[tex]\dfrac{3}{5}\times7500=3\times1500=4500[/tex]

Now, the number of people chose Pepsi = 7,500-4,500=3,000

Hence, there are 3,000 people who chose Pepsi.

Explain why you would want to keep some, but not all, receipts as part of your financial records.

Answers

You or we keep only those receipts

1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.

2. We keep those receipts of goods,which are under warranty period or for which you are paying EMI.

3.  Receipt of those goods which has very high amount printed on it, and it mismatch with our income ,i.e not correlated with our income Someone can make false claim to entangle you.

Answer:

1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.

Step-by-step explanation:

A ratio is a rate. Sometimes always or never true

Answers

By definition, the ratio is the expression that would allow us to express the quotient of two numbers and/or any mathematical expressions. Let us take for example, numbers 4 and 5. The ratio between these values is 4/5. 

The statement given above, "A ratio is a rate" is only sometimes true. This is only true when the unit of measurement of the denominator is in terms of time (seconds, minutes, hours, years, etc) because this would tell us how fast is something being done, consumed, etc. Example, the speed or rate of a car is 4 meters / 5 seconds.


































One serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams from other sources. How many grams of protein do you need daily?

Answers

48 grams= 96% needed

x grams. = 4%

Set up a proportion

48/96 = x/4

96/24=4
48/24=2
x=2= grams in the granola

Add the value of 96% and the value of 4% to get the value of 100%

2+48=50

Final answer: 50 grams

Simplify x^2-4x-32/x^2+7x+12

Answers

It equals to:

(x - 8)(x + 4) / (x+3)(x+4)

If x ≠ -4

Then it equals to:

(x-8) / (x+3)
Simplify x^2-4x-32/x^2+7x+12
Answer see form:


1) Which number rounds up when rounded to the nearest tenth?

55. 24

170.93

0.12

8.15

___________

2)

Estimate the value of 2968 + 9912 by rounding each number to the thousands.

14,000

13,000

12,000

7000
___________

3)

Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4

25 times 4 = 100

30 times 5 = 150

27 times 4 = 108

20 times 4 = 80
_____________
4)

Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.

30

33

123

130
___________
5)

Determine which answer is reasonable for 4. 8 times 9.2.

14

45.36

432

870.4

Answers

1)8.15
2)13,000
3)25 x 4 =100
4) 130
5)45.36

Answer:

1)8.15

2)13,000

3)25 x 4 =100

4) 130

5)45.3

Step-by-step explanation:

Grape juice comes in a 64 oz bottle. Apple juice comes in a 80 ounce bottle. Both juices will be poured into cups of equal size so that no juice remains in either bottle. How many ounces is the largest possible cup that can be used for both juices?

Answers

an 80 ounce cup i may be wrong

A pilot can fly an airplane 2240 miles with the wind in the same time as she can fly 1920 miles against the wind. If the speed of the wind is 40 mph, find the speed of the plane in still air.

Answers

recall your d = rt, distance = rate * time

so... hmm if the plane has a still air speed of say "r", when it's going with the wind, is not really going "r" fast, is going "r + 40 ", because the wind is adding 40mph to its speed, is really moving.

and when the plane is going against the wind, is not really going "r" fast either, is going " r - 40 ", because the wind is eroding speed from it.

now, it went 2240 miles for say "t" hours, and it did 1920 miles for the same length of time, "t" hours.

[tex]\bf \begin{array}{lccclll} &distance&rate&time\\ &-----&-----&-----\\ \textit{with the wind}&2240&r+40&t\\ \textit{against the wind}&1920&r-40&t \end{array} \\\\\\ \begin{cases} 2240=(r+40)t\implies \frac{2240}{r+40}=\boxed{t}\\ 1920=(r-40)t\\ ----------\\ 1920=(r-40)\left( \boxed{\frac{2240}{r+40}} \right) \end{cases} \\\\\\ 1920=\cfrac{(r-40)2240}{r+40}\implies 1920(r+40)=(r-40)2240 \\\\\\ 1920r+76800=2240r-89600\implies 166400=320r \\\\\\ \cfrac{166400}{320}=r[/tex]

and surely you know how much that is.

Find AB if BC = 4 , BD = 5, and AD =4

Answers

I think there could be many solutions but one is B=1 C=4 D=5 A=0.8 so AB=0.8

16. Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.

Answers

Number of days of the week = 7 days

Decrease rate of the dosage = 20 mg / day

Total decrease = number of days * decrease rate per day = 7 days * 20 mg / day

Total decrease = 140 mg.

Answer: total decrease in Tamara's medication ant the end of the week is 140 mg.

Scotty is planning to order 1 cubic yard of topsoil for his 15' by 24' garden expecting that if evenly spread, he would end up with 2 inches of topsoil. Is he correct? Explain.

Answers

2 inches = 0.1666 feet

15 x 24 x 0.1666 = 59.98 cubic feet

 1 cubic yard = 27 cubic feet

59.98 is greater than 27 so 1 cubic yard of topsoil will not be enough

Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by the xy-plane.

Answers

[tex]\displaystyle\iiint_R\mathrm dV=\int_{y=-7}^{y=7}\int_{x=-\sqrt{49-y^2}}^{x=0}\int_{z=x}^{z=0}\mathrm dz\,\mathrm dx\,\mathrm dy[/tex]

Converting to cylindrical coordinates, the integral is equivalent to

[tex]\displaystyle\iiint_R\mathrm dV=\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}\int_{z=r\cos\theta}^{z=0}r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_{\theta=\pi/2}^{\theta=3\pi/2}\int_{r=0}^{r=7}-r^2\cos\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=-\displaystyle\left(\int_{\theta=\pi/2}^{3\pi/2}\cos\theta\,\mathrm d\theta\right)\left(\int_{r=0}^{r=7}r^2\,\mathrm dr\right)[/tex]
[tex]=\dfrac{2\times7^3}3=\dfrac{686}3[/tex]

We have that

Volume of the  wedge-shaped region

[tex]W=228.65[/tex]

Attached below is a picture of the wedge-shaped region contained in the cylinder

Bearing in mind this shape, we have that the coordinates identifying the cylinder are as follows

Co-ordinates

[tex]0 \leq r \leq 7,\frac{\pi}{2} \leq 0 \leq \frac{\pi}{2},0 \leq z \leq x[/tex]

Where

[tex]0 \leq z \leq x =rcos \phi[/tex]

Generally the equation for the volume of the  wedge-shaped region W  is mathematically given as

[tex]\int \int \int_W 1dv=\int^{7}_{0} \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \int^{rcos \phi}_{0}[/tex]

[tex]\int \int \int_W 1dv=\int^{7}_{0} r (\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}}rcos\phi dv))dr[/tex]

[tex]\int \int \int_W 1dv=(\frac{(7)^3}{3}+\frac{(0)^3}{3})(sin {\pi/2}+sin{-\pi/2})[/tex]

[tex]\int \int \int_W 1dv=228.67[/tex]

Therefore

Volume of the  wedge-shaped region

[tex]W=228.65[/tex]

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The function f(x)=log[7]x is increasing. True or false

Answers

I would say that the answer is true

The given function increases as x increases, so the statement is true.

Is the function increasing?

Here we have the function:

[tex]f(x) = log_7(x)[/tex]

To see if it is increasing, we can evaluate in two values, 10 and 15, this will serve to see if the function is increasing or not:

[tex]f(10) = log_7(10) = 1.18\\\\f(15) = log_7(15) = 1.39[/tex]

As you can see, when x increases also does f(x), so the function is increasing.

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An investigator wants to estimate caffeine consumption in high school students. how many students would be required to estimate the proportion of students who consume coffee? suppose we want the estimate to be within 5% of the true proportion with 95% confidence.

Answers

We can solve this problem by referring to the standard probability distribution tables for z.

We are required to find for the number of samples given the proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value of z equivalent to:

z = 1.96

Since the problem states that it should be within the true proportion then p = 0.5

Now we can find for the sample size using the formula:

n = (z^2) p q /E^2

where,

 p = 0.5

q = 1 – p = 0.5

E = estimate of 5% = 0.05

Substituting:

n = (1.96^2) 0.5 * 0.5 / 0.05^2

n = 384.16

Around 385students are required.

a commercial jet airplane climbs at takeoff with slope m=4/9. How far in the horizontal direction will the airplane fly to reach am altitude of 20,000 ft above the takeoff point?

Answers

[tex]\bf slope = {{ m}}= \cfrac{rise}{run}\implies \cfrac{\textit{vertical direction}}{\textit{horizontal direction}}\implies \cfrac{4}{9}=\cfrac{20000}{h}[/tex]

solve for "h".

The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.

What is a linear equation?

A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A commercial jet airplane climbs at takeoff with slope m = 4/9.

Then the equation of the line will be given as,

y = (4/9)x

The y-intercept is zero.

The horizontal direction will the airplane fly to reach an altitude of 20,000 ft above the takeoff point will be

20,000 = (4/9)x

180,000 = 4x

x = 180,000 / 4

x = 45,000 feet

The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.

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The area of a rectangle is 27 m^2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
Length: ___m
Width: ____m

Answers

Let [tex]L[/tex] be the length of the rectangle and [tex]W[/tex] be the width. In the problem it is given that [tex]L=2W-3[/tex]. It is also given that the area [tex]LW=27[/tex]. Substituting in the length in terms of width, we have [tex]W(2W-3)=27 \\ 2W^2-3W-27=0 \\ (2W-9)(W+3)=0[/tex]. Using the zero product property, [tex]2W-9=0 \text{ or } W+3=0[/tex]. Solving these we get the width [tex]W=4.5 \text{ or } -3[/tex]. However, it doesn't make sense for the width to be negative, so the width must be [tex]\boxed{4.5 \text{ m}}[/tex]. From that we can tell the length [tex]L=2(4.5)-3=\boxed{6 \text{ m}}[/tex]. 

The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism? a base area of 4y square units and height of 4y2 + 4y + 12 units a base area of 8y2 square units and height of y2 + 2y + 4 units a base area of 12y square units and height of 4y2 + 4y + 36 units a base area of 16y2 square units and height of y2 + y + 3 units

Answers

base 16y^2
height y^2 + y + 3
V = b*h
V = 16y^2(y^2 + y + 3)
V = 16y^4 + 16y^3 + 48y^2
Last option

Answer:

D!

a base area of 16y2 square units and height of y2 + y + 3 units

A square is inscribed in a circle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.

Answers

Let x = side length of the square and d = diameter of the circle
d also is the hypotenuse of the square

Through the pythagorean theorem, we know that
x^2 + x^2 = d^2
2x^2 = d^2

Because d = 2r, this means
2x^2 = d^2
2x^2 = (2r)^2
2x^2 = 4r^2
x^2 = 2r^2

The area of the square is x^2, which is the same as 2r^2 as shown above

The area of the circle is A = pi*r^2

Divide the area of the square over the area of the circle to get
(x^2)/(pi*r^2) = (2r^2)/(pi*r^2) = 2/pi

The exact answer, in terms of pi, is the fraction 2/pi

If you want an approximate answer, then use a calculator to get roughly 0.6366 which is about 63.66%

The probability of the point will be in the shaded region is 0.64 or 64%.

A square is inscribed in circle. Probability of point to be pick from the square to be find out.

What are Venn diagram?

Venn diagram are the Figures of probabilities to understand better.

Here, diameter of circle = d and radius r =d/2, edge of the square = a
By Pythagorean theorem,
a²+a²=d²
2a²= (2r)²
a²=2r²
Area of the square =2r²
Area of the circle = πr²
Now probability = Area of the square/Area of the circle
                        = 2r²/πr²
                        = 2/π
                        = 0.64

Thus, The probability of the point will be in the shaded region is 0.64 or 64%.

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A ship traveled at an average rate of 22 miles per hour going west. It then traveled at an average rate of 12 miles per hour heading north. If the ship traveled a total of 158 miles in 9 hours, how many miles were traveled heading north?

Answers

Tw = Time traveled west
Tn = Time traveled north
Tw + Tn = 9 hours
22Tw + 12Tn = 158 miles
Solve the 2 equations and you get
Tw = 5 hours
Tn = 4 hours
12 x 4 = 48 miles traveled north

Most teachers enjoy teaching students. Most teachers are college graduates. Assuming these two statements are true, do some college graduates enjoy teaching students?

Answers

in the two given statements we can conclude that yes some college graduates do indeed teaching students.

Answer:

yes some some college graduates enjoy teaching students.

Step-by-step explanation:

This question is based on reasoning.

Most teachers enjoy teaching students.

Most teachers are college graduates.

A syllogism is a form of logical reasoning formed by the joining of two or more premises to arrive at a conclusion.

So, here we can say that yes some some college graduates enjoy teaching students.

Three students simplified the expression 2x- 3(y-2x) +-5times -2y.
Amber -4y + 7y
Butch 4x + 7y
Carl 8x + 7y

Who is correct? Explain the error the other students made

Answers

Carl is right because simplifying it gets us: [tex]2x-3y+6x+10y=8x+7y[/tex]

If the revenue for the week is $2000, and labor cost consist of two workers earning $8 per hour who works 40 hours each, whay is labor cost aa percentage of revenue?

Answers

two workers earning 8 bucks an hour for 40hrs, well, that means each worker is making 8*40 or 320 bucks, now, is two workers, so 320+320 or 640 is the total cost then.

now, the revenue, sales income, is 2,000 bucks, how much is 640 off of?

well, if we take 2000 to be the 100%, what is 640 in percentage off of it?

[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 2000&100\\ 640&x \end{array}\implies \cfrac{2000}{640}=\cfrac{100}{x}[/tex]

solve for "x".

The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the rectangular prism is square units.

Answers

Given:

The volume of the rectangular prism is 

[tex] b^{3}+8 b^{2} +19b+12 [/tex],

the height is h=(b+3)

1. The volume of a rectangular prism is (base area)*height

also, notice that the volume is a third degree polynomial, the height is a 1st degree polynomial, so the base area must be a 2nd degree polynomial, whose coefficients we don't know yet.
Let this quadratic polynomial be [tex](mb^{2}+nb+k)[/tex]

 
2

[tex]b^{3}+8 b^{2} +19b+12=(mb^{2}+nb+k)*(b+3)[/tex]


notice that  [tex]b^{3}[/tex] is the product of the largest 2 terms: [tex]mb^{2}[/tex] and b, so m must be 1

also, notice that 12 is the product of the constants, k and 3

so k*3=12, this means k=4

3
we write the above equality again:

[tex] b^{3}+8 b^{2} +19b+12=(b^{2}+nb+4)*(b+3)[/tex]


[tex](b^{2}+nb+4)(b+3)= b^{3}+3 b^{2} +nb^{2}+3nb+4b+12[/tex]

=[tex]= b^{3}+(n+3)b^{2}+(3n+4)b+12[/tex]


4
now compare the coefficient with the left side:

[tex]8 b^{2}=(n+3)b^{2}[/tex]

8=n+3

n=5


substituting n=5: 

the base area is [tex]b^{2}+5b+4 [/tex]

Answer: [tex]b^{2}+5b+4 [/tex]


Answer:

b^2 + 5b +4

Step-by-step explanation:

Given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.

(A ) - {}
(B) - {a,e}
(C ) - {a, b, e, g, i, l, o, r, u}

Answers

The unition of two sets [tex]A[/tex] and [tex]B[/tex], written [tex]A\cup B[/tex], is that set containing all elements in either [tex]A[/tex] or [tex]B[/tex] (or both, since "or" is taken as inclusive here) i.e.:

[tex]A\cup B=\{x|x\in A \lor x\in B\}[/tex]

Thus:
[tex]A\cup B=\{a,e,i,o,u\}\cup\{a,l,g,e,b,r\}[/tex]
[tex]A\cup B[/tex]={a,b,e,g,i,l,o,r,u}
The union of two sets is a new set that contains all of the elements from those 2 sets

A ∪ B = {a, b, e, g, i, l, o, r, u}

answer

(C ) - {a, b, e, g, i, l, o, r, u}

What is the estimate of 462,809+256,738

Answers

Hi, 
the estimate would be... 
500,000 + 300,000
your answer would be: 800,000.

I hoped I helped and if you need more you could always ask me :)
-Dawn

Find the taylor polynomial t3(x) for the function f centered at the number

a. f(x) = e^(â3x) sin(2x), a = 0

Answers

[tex]e^{-3x}=\displaystyle\sum_{n=0}^\infty\frac{(-3x)^n}{n!}=1-3x+9x^2+\cdots[/tex]
[tex]\sin2x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^n(2x)^{2n+1}}{(2n+1)!}=2x-\dfrac{4x^3}3+\cdots[/tex]

[tex]e^{-3x}\sin2x=\left(1-3x+9x^2+\cdots\right)\left(2x-\dfrac{4x^3}3+\cdots\right)[/tex]
[tex]\approx T_3(x)=(1-3x+9x^2)\left(2x-\dfrac{4x^3}3\right)[/tex]
[tex]T_3(x)=2x-6x^2+\left(18-\dfrac43\right)x^3[/tex]
[tex]T_3(x)=2x-6x^2+\dfrac{50}3x^3[/tex]

A tape that records one hour and 30 minutes on each side moves at cm a second through the tape player. How long, in metres, is the tape?

Answers

The tape is 54 meters long, seeing as 90 minutes=5400 seconds and 5400 centimeters divided by 100 equals 54 ergo 54 meters is your answer
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