1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
salantis [7]
3 years ago
13

The sum of the angle measures of any triangle is 180 degrees. find the angle measures of a triangle if the second angle measures

twice the first, and the third angle measures 15 degrees less than the second.
Mathematics
1 answer:
MissTica3 years ago
3 0
A+b+c= 180
<span>a = ?
</span><span>b = 2a - 10 (twice a minus 10)
</span><span>c = b + 25 (25 more than b)
</span><span>Substitute for b
c = (2a-10) + 25
</span><span>Now substitute back into a+b+c=180
a + (2a-10) + (2a-10+25) = 180
</span><span>Eliminate the parentheses
a + 2a - 10 + 2a - 10 + 25 = 180
</span><span>Combine like terms
5a + 5 = 180
</span><span>Subtract 5 from both sides
5a = 175
</span><span>Divide both sides by 5
a = 35
</span><span>Substitute into the equation for b.
b = 2a -10 = 2*35 - 10 = 70 - 10 = 60
</span><span>Add 25 to b to get c.
c = 60 + 25 = 85</span><span>Check by adding them up.
35 + 60 + 85 = 180
Done.</span>
You might be interested in
"The last time I bought this product, it cost $20.00 but it looks like it costs $29.60 today. Why such a large increase?"
Oksanka [162]

Answer:

The company decided to increase the price by $9.60, or by 48%.

Step-by-step explanation:

To measure the price difference in dollars is simple, just subtract the old price from the new one:

29.60 - 20 = 9.60

Divide the price change by the old price to find the price increase in percentage:

9.60 \div 20 = 0.48 \\ 0.48 \times 100\% = 48\%

5 0
3 years ago
Entry function to model the situation. Then find the value of the function after the given amount of time. Use T as your variabl
steposvetlana [31]

Answer:

her salary after 8 years is $26,602

Step-by-step explanation:

Given that

Fiona salary is $21,000

She received 3% raise each year

We need to find her salary after 8 years

So, here we apply the future value formula

i.e.

= Present value × (1 + rate of interest)^number of years

= $21,000 × (1 + 0.03)^8

= $21,000 × 1.03^8

= $26,602

hence,  her salary after 8 years is $26,602

3 0
3 years ago
The equation $1.50p + $5.00 = $14.00 shows the total cost of picking p pounds of blueberries at a local blueberry farm. How many
julia-pushkina [17]
First we need to subtract $5 from both sides.  That gives us the new equation 1.50p = 9.  Then, divide 9 by 1.5, which gives you the answer.  9/1.5 = 6.  
8 0
3 years ago
if rectangle ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180 degrees, where would point A lie. ​
cupoosta [38]

Answer: Point A would be at (1,-1)

3 0
3 years ago
Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviati
Gennadij [26K]

Answer:

a. the probability that her pulse rate is less than 76 beats per minute is 0.5948

b. If 25 adult females are randomly​ selected,  the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849

c.   D. Since the original population has a normal​ distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

Given that:

Mean μ =73.0

Standard deviation σ =12.5

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is less than 76 beats per minute.

Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.

Then : X \sim N ( μ = 73.0 , σ = 12.5)

The probability that her pulse rate is less than 76 beats per minute can be computed as:

P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})

P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})

P(X < 76) = P(Z< \dfrac{3}{12.5})

P(X < 76) = P(Z< 0.24)

From the standard normal distribution tables,

P(X < 76) = 0.5948

Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948

b.  If 25 adult females are randomly​ selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.

now; we have a sample size n = 25

The probability can now be calculated as follows:

P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})

P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})

P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})

P( \overline X < 76) = P(Z< 1.2)

From the standard normal distribution tables,

P(\overline X < 76) = 0.8849

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

In order to determine the probability in part (b);  the  normal distribution is perfect to be used here even when the sample size does not exceed 30.

Therefore option D is correct.

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

5 0
3 years ago
Other questions:
  • I need to know long division better
    7·2 answers
  • Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre
    6·1 answer
  • Identify the percent, amount, and base in this problem: 30% of what number is 75?
    15·2 answers
  • You need to order carpet for a room that has a length that is twice its width. if the area of the room is 450, find the width of
    15·1 answer
  • Toyland is having a sale all items are 20% off how much will you save on an item that usually sells for $45.
    13·2 answers
  • Bobby bought 3 5/12 ft of red ribbon and 5 1/12 ft of yellow ribbon. ribbon costs $1.20 a foot. How much did Bobby spend on ribb
    15·1 answer
  • A map has a scale of 4cm. to 12 km. what distance does 16 cm represent
    5·1 answer
  • Plssssss help number 18 and 20​
    5·2 answers
  • Please help I need help! This is the only way I will pass this unit
    5·2 answers
  • What is y = –3(x – 3)(x + 7) in standard form ?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!