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nikklg [1K]
1 year ago
13

Evaluate. 58−(14)2=58-142= ________

Mathematics
1 answer:
nasty-shy [4]1 year ago
7 0

For this case we have the following expression:

58- (14) ^ 2

The first step is to solve the quadratic term.

We have then:

58- (14) ^ 2 = 58-196

Then, the second step is to subtract both resulting numbers:

58- (14) ^ 2 = -138

We observe that the result obtained is a negative number.

Answer:

The result of the expression is given by:

58- (14) ^ 2 = -138

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Tommy Webster obtained a 30-year, $110,000.00 mortgage loan from People's Savings. The interest rate is 7.5 percent. For the fir
Pepsi [2]
The interest on the first monthly payment is ...
  I = Prt
  I = 110,000*7.5%*(1/12)= 687.50

For the first payment, the interest is
  $687.50

_____
The time period for the interest rate calculation is 1/12 year.
4 0
2 years ago
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Ksju [112]
Well, here's one way to do it at least... 

<span>For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). </span>

<span>Let P=(4,0) be the projection of B onto the x-axis. </span>
<span>Let Q=(-3,0) be the projection of C onto the x-axis. </span>

<span>Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). </span>

<span>Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). </span>

<span>Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. </span>

<span>||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) </span>
<span>||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) </span>

<span>Using the Law of Cosines... </span>
<span>||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) </span>
<span>||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) </span>
<span>||a||^2 = 86 - 36 </span>
<span>||a||^2 = 50 </span>
<span>||a|| = sqrt(50) </span>

<span>Now apply the Law of Sines to find the other two angles. </span>

<span>||b|| / sin(B) = ||a|| / sin(A) </span>
<span>sqrt(41) / sin(B) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(41) / sqrt(50) = sin(B) </span>
<span>.8222 = sin(B) </span>
<span>asin(.8222) = B </span>
<span>55.305 = B </span>

<span>Two down, one to go... </span>

<span>||c|| / sin(C) = ||a|| / sin(A) </span>
<span>sqrt(45) / sin(C) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(45) / sqrt(50) = sin(C) </span>
<span>.8614 = sin(C) </span>
<span>asin(.8614) = C </span>
<span>59.470 = C </span>

<span>So your three angles are: </span>

<span>A = 65.225 </span>
<span>B = 55.305 </span>
<span>C = 59.470 </span>
8 0
1 year ago
Translate and solve: seventy-eight times n is at least 312.
RideAnS [48]

It translates to 78n \ge 312 which solves to n \ge 4 after dividing both sides by 78. This means n is equal to 4 or it can be larger than 4.

7 0
1 year ago
A circle fits inside a semicircle of diameter 24mm
patriot [66]

Answer:

The shaded are is 113\ mm^{2}

Step-by-step explanation:

we know that

The shaded area is equal to the area of the semicircle minus the area of the circle inside the semicircle

step 1

Find the area of semicircle

The area of semicircle is equal to

A=\frac{1}{2}\pi r^{2}

where

r=24/2=12\ mm ----> the radius is half the diameter

substitute

A=\frac{1}{2}\pi(12)^{2}=72\pi\ mm^{2}

step 2

Find the area of the circle inside the semicircle

The area of circle is equal to

A=\pi r^{2}

where

r=12/2=6\ mm ---> the radius of circle inside is half the radius of semicircle

substitute

A=\pi(6)^{2}=36\pi\ mm^{2}

step 3

Find the shaded area

72\pi\ mm^{2}-36\pi\ mm^{2}=36\pi\ mm^{2}

assume

\pi=3.14

36(3.14)=113.04\ mm^{2}

3 significant figures is

113\ mm^{2}

6 0
1 year ago
The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.512.512, point, 5 years; the stan
zaharov [31]

This question was not written properly

Complete Question

The lifespans of lions in a particular zoo are normally distributed. The average lion lives 12.5 years; the standard deviation is 2.4 years. Use the empirical rule (68-95-99.7\%)(68−95−99.7%) to estimate the probability of a lion living between 5.3 to 10. 1 years.

Answer:

Thehe probability of a lion living between 5.3 to 10. 1 years is 0.1585

Step-by-step explanation:

The empirical rule formula states that:

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

3) 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

Mean is given in the question as: 12.5

Standard deviation : 2.4 years

We start by applying the first rule

1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.

μ - σ

12.5 -2.4

= 10.1

We apply the second rule

2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.

μ – 2σ

12.5 - 2 × 2.4

12.5 - 4.8

= 7.7

We apply the third rule

3)99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.

μ - 3σ

= 12.5 - 3(2.4)

= 12.5 - 7.2

= 5.3

From the above calculation , we can see that

5.3 years corresponds to one side of 99.7%

Hence,

100 - 99.7%/2 = 0.3%/2

= 0.15%

And 10.1 years corresponds to one side of 68%

Hence

100 - 68%/2 = 32%/2 = 16%

So,the percentage of a lion living between 5.3 to 10. 1 years is calculated as 16% - 0.15%

= 15.85%

Therefore, the probability of a lion living between 5.3 to 10. 1 years

is converted to decimal =

= 15.85/ 100

= 0.1585

8 0
2 years ago
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