Answer:
Sarah is correct
Step-by-step explanation:
Required
Which of the students is correct
Let a number be x,
Given what the teacher asked the students to do, the solution is:
[tex]Number = x[/tex]
[tex]Opposite = -x[/tex]
[tex]Absolute = |x|[/tex]
Only Sarah got this correctly; others are incorrect.
The proof is as follows.
For Sarah
[tex]Number = 1416[/tex]
[tex]Opposite = -1416[/tex]
[tex]Absolute =|1416| = 1416[/tex]
So, the numbers will be: 1416, -1416 and 1416
Other students are incorrect
Justine earned a total lifetime income of
$1,050,000 as a flight attendant. Her sister
Abigail earned a total lifetime income of
$4,800,000 as an attorney. If each sister worked
for 30 years, how much greater was Abigail's
annual salary than Justine's?
Answer:
$125,000
Step-by-step explanation:
In 30 years, Abigail earned the following amount more than Justine:
$4,800,000 - $1,050,000 = $3,750,000
Per year, the difference is
$3,750,000/30 = $125,000
Answer: $125,000
Suppose you work for a large coffee distributor that has a secret coffee blend it sells to local stores. You mix the Gazebo blend with the Mexican Shade Grown blend, but always in the same proportion. Yesterday, you mixed 90 pounds of the Gazebo blend with 27 pounds of the Mexican Shade Grown blend. Today, there is 60 pounds of the Gazebo coffee left in stock. How many pounds of the Mexican Shade Grown coffee should you mix with it to get your secret blend?
Answer:
18lbs of Mexican Shade Grown coffee
Step-by-step explanation:
Since this is a ratio problem and we are given three values and one variable x (pounds of Mexican Shade Grown coffee needed) we can use the Rule of Three to solve this problem. In this rule we simply multiply the diagonal available values and divide by the third value to get the value of the variable, like so...
90lbs Gazebo <=====> 27lbs Mexican Blend
60lbs Gazebo <=====> x lbs Mexican Blend
(60 * 27) / 90 = x
1620 / 90 = x
18 lbs = x
We need 18lbs of Mexican Shade Grown coffee blend to mix with the 60lbs of Gazebo blend
Find the volume of the prism
The area of a rectangular wall of a barn is 54 feet. It’s length is 12 feet longer than twice it’s width. Find the length and width of the wall of the barn.
Answer:the width is 3 feet
Step-by-step explanation:
Determine center point and radius in the equation x^2+y^2-6y+1=0
9514 1404 393
Answer:
center: (0, 3)radius: 2√2Step-by-step explanation:
The equation can be put into standard form by "completing the square" for each variable. The x-term is already a square, so we need do this only for the y-term.
x^2 +(y^2 -6y) = -1
x^2 +(y^2 -6y +9) = -1 +9 . . . . . . add (-6/2)^2 to complete the square
x^2 +(y -3)^2 = 8 . . . . standard form equation
__
Comparing the above equation to the form:
(x -h)^2 +(y -k)^2 = r^2 . . . . . . . circle centered at (h, k), radius r
we see that (h, k) = (0, 3) and r^2 = 8 ⇒ r = 2√2.
The center point is (0, 3); the radius is 2√2.
Write your answer using integers, proper fractions, and improper fractions in the simplest form
PLEASE HELP
Answer:
y = 1/4 x - 7/2
Step-by-step explanation:
x - 4y = 14
-4y = -x + 14
y = -x/(-4) - 14/4
y = 1/4 x - 7/2
May you solve this for me?
Answer: 23.94 cm
Step-by-step explanation: I am totally not sure if this is the answer, but think of it this way: Those are 2 semi circles. The formula for the area of a semi circle is A = π * r^2 / 2. For the semi circle with 6 cm, the radius is 3. So we can plug it in the formula. 3.14 * 3^2 / 2, which is 14.13. For the semi circle with 5 cm, the radius is 2.5. Again plug it in and it will be 3.14 * 2.5^2 / 2, which is 9.8125. Then, to get the total area, add the 2 final values together. 9.8125 + 14.13, which is 23.9425. Then it said "round to the nearest hundredth if necessary. We can round to the nearest hundredth, which is 23.94, so that would be the answer. That is just my thought process.
I am not really sure if it's the answer, but take a gander at my thought process and hopefully, you can agree with me.
What is the area of the triangle?
Pls help extra points and mark brainlist

Answer:
(3,2)
Step-by-step explanation:
...................
Rewrite each of the following expressions as powers with a base of 2
Answer:
Step-by-step explanation:
what expressions?
Need answer asap, will give brainliest.
The solution is the point where the lines cross. So (-1, -2)
The radius of a circle is 13 cm. Find its circumference in terms of pie.
Answer:
26 pi
Step-by-step explanation:
Answer:
531
Step-by-step explanation:
first the formula for finding the circumference of a circle is πr2
where π = 22/7
r = 13x13
hence, circumference = πr2
= 22/7 x 13 x 13
= 22/7 × 169
= 22 x 169/7
= 3718/7
= 531 cm
tour busload of 45 people attended two Florida theme parks on successive days. On Day 1 the entrance fee was $15 per adult, $8 per child, $12 per senior citizen and the total charge was $558. On Day 2 the entrance fee was $20 per adult, $12 per child, $17 per senior citizen and the total charge was $771. How many adults, children, and senior citizens were on this tour bus
Answer: There are 22 adults , 12 children and 11 senior citizens on the tour bus.
Step-by-step explanation:
Let adult = x
children = y
senior citizen = z
Given : Total busload (x+ y + z) = 45
Total charge on day 1 = 558 $ = [tex]15\times x+8\times y+12\times z[/tex]
Total charge on day 2 = 771 $ = [tex]20\times x+12\times y+17\times z[/tex]
Now we have 3 equations : x+ y+z =45
[tex]15\times x+8\times y+12\times z=558[/tex]
[tex]20\times x+12\times y+17\times z=771[/tex]
Solving for them we get: x= 22 , y = 12 and z= 11
Thus there are 22 adults , 12 children and 11 senior citizens.
what is the approximate height of h?
A father is questioning the probability his daughter will receive a scholarship. She is a finalist for two different scholarships. The awarding of these scholarships is independent. For the first scholarship (Scholarship A) there are 5 finalists and two scholarships will be awarded. For the second scholarship (Scholarship B) there are also five finalists and one scholarship will be awarded.
1. What is the probability that she will receive Scholarship A and Scholarship B?
2. What is the probability that she will receive at least one scholarship, Scholarship A or Scholarship B?
3. Should she apply for both scholarships or one of the scholarships? If just one, which one? Why?
Solution :
According to the question, let
A : winning first scholarship
B : winning second scholarship
So for the first scholarship, there are five finalist and only two scholarship will be awarded. And for the second scholarship there are five finalist and only one scholarship will be awarded.
Therefore,
[tex]$P(A)=\frac{2}{5}$[/tex] and [tex]$P(B)=\frac{1}{5}$[/tex]
1. So, [tex]$P(A \cap B ) = P(A) P(B)$[/tex]
[tex]$=\frac{2}{5} \times \frac{1}{5}$[/tex]
[tex]$=\frac{2}{25}$[/tex]
2. [tex]$P(A \cup B) = P(A)+P(B)-P(A)P(B)$[/tex]
[tex]$=\frac{2}{5}+\frac{1}{5}-\frac{2}{25}$[/tex]
[tex]$=\frac{13}{25}$[/tex]
3. She should apply to both the scholarships, so as to have a maximum chances of winning at least one scholarship.
Plz someone answer I will give u points
Answer:
FL = 54°
Step-by-step explanation:
m<MNF = ½(ML + LF) (inscribed angle theorem)
7 + 8x = ½(72 + 7x + 5)
Solve for x
2(7 + 8x) = 72 + 7x + 5
14 + 16x = 72 + 7x + 5
Add like terms
14 + 16x = 77 + 7x
16x - 7x = 77 - 14
9x = 63
x = 63/9
x = 7
✅FL = 7x + 5
Plug in the value of x
FL = 7(7) + 5 = 49 + 5
FL = 54°
Solve for Y= 1680 + 0.72
Please help, will give 14 points.
Answer:
25
Step-by-step explanation:
count the frequencies so to get your answer. It is 25.
if it helps don't forget to like and mark me down
which one of yu geniuses can answer this question ???
Answer:
B. 20
Step-by-step explanation:
x + 40 = 3x
x - x + 40 = 3x - x
40 = 2x
20 = x
In a school of 1200 students, the ratio of
the number of teachers to students is 1 : 15.
After some teachers join the school, the ratio of
the number of teachers to students becomes 3:40.
Find
(i) the initial number of teachers in the school,
(ii) the number of teachers who join the school.
Step-by-step explanation:
i)Initial School population,
given 15 units = 1200
1 unit =
[tex]1200 \div 15 \\ = 80[/tex]
Number of teachers (initial) = 1 unit = 80.
ii)take j = number of teachers joining the school.
New teacher population = 80+j
[tex] \frac{3}{43} (1280 + j) = 80 + j \\ \frac{3840}{43} + \frac{3}{43} j = 80 + j \\ j - \frac{3}{43} j = \frac{3840}{43} - 80 \\ \frac{40}{43} j = \frac{400}{43} \\ 40j = 400 \\ j = 400 \div 40 \\ = 10[/tex]
A composite figure is shown below.
What is the area of the composite figure?
12 in.
0204 square inches
222 square inches
3 in.
5 in.
228 square inches
4 in. 4 in.
234 square inches
24 in.
8 in.
Answer:
234 square inches
Step-by-step explanation:
Ok take this shape step by step. First solve the rectangle.
The area of the rectangle would be: 24 * 8 = 192
Rectangle Area: 192
Then, solve the area for the triangle in the middle.
The area of that triangle would be: 8 * 3 divided by 2. You get 8 by the base of the triangle, 4 + 4. 3 is of course, the height. Lastly, you divide this by 2 because that is the formula for the area of a triangle. When you solve, you get 12.
Middle Triangle Area: 12
Then solve for the last triangle.
Doing the same thing, the area for that triangle is 12 * 5 divided by 2. So solve, 12*5 = 60, 60/2 = 30
Last Triangle area: 30
Finnally, add all the areas up,
192 + 12 + 30 = 234
What is the value of y ?
[tex]y^{2}=6*(6+2)\\\\y^{2}=48\\\\4\sqrt{3}[/tex]
1. Noah has $15,000 to invest. He invests some amount at 5% annual interest and the rest at 3% annual
interest. After one year, his total interest from both accounts is $620.
How much did he invest in each account? (Clearly label which amount is for which account in your
answer. Hint: Over a one year period, annual interest is the same as simple interest.)
[6 pts]
Answer:
He invested $ 8500 at the interest of 5% and $ 6500 at the interest of 3%
Step-by-step explanation:
Let the sum invested at interest rate of 5% be X
Let the sum invested at interest rate of 3% be Y
As we know
[tex]X + Y = 15000[/tex] - Eq (1)
[tex]X* 5/100 *1 + Y * 3/100 * 1 = 620[/tex]
[tex]5X + 3Y = 62000[/tex] ---Eq (2)
Multiplying Eq (1) by 3 we get -
[tex]3X + 3Y = 45000[/tex]
Substract Eq (1) from Eq (2) we get
[tex]5X + 3Y = 62000\\- 3X -3Y = -45000\\2X = 17000\\X = 8500\\Y = 15000-8500 = 6500[/tex]
He invested $ 8500 at the interest of 5% and $ 6500 at the interest of 3%
Write the fraction as BOTH percentages and decimals.
114/165
Answer: 69.09% is the percentage. 0.6909 is the decimal
Step-by-step explanation:
hope this helps! you don't have to but maybe mark as brainliest?
20% of 150 is of what
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
150 x .2 = 30
Estimate the area of the circle. Use 7/22 for π
Answer:
Area = pi * r^2
r is half of the diameter
Area = pi * 14^2
Area = 196 pi
196 * 3.14
Area is approximately 615.44 cm^2
PLEASE HELP ME ANYONE :(
Answer
B
Step-by-step explanation:
5*5*6=150
Answer:
150
Step-by-step explanation:
two numbers add up to 144. one number is half the square of the other number. what are the numbers
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Answer:
36 plus 36 plus 72 = 144 or 72 + 72= 144
i will award brainliest HELPP
Answer:
D
Step-by-step explanation:
Z - ( -7 ) < 5 it’s solving inequalities. Help. Also 8(3g - 2) <= 12(2g + 1) pls ;-;
Answer:
z < -2
g is indeterminate
Step-by-step explanation:
For the inequality Z - ( -7 ) < 5
open the parenthesis
z+7 < 5
Subtract 7 from both sides
z+7-7 < 5-7
z < -2
For 8(3g - 2) <= 12(2g + 1)
Expand
24g -16 ≤ 24g + 12
24g - 24g ≤ 12+18
0g≤ 28
g ≤ 28/0
Hence g is indeterminate