Hello there.
To answer this question, we need to remember some properties of the isosceles triangle.
First (and most importantly), an isosceles triangle is composed by three sides, in which only two of the sides have equal length.
The perimeter of a triangle is given by the sum of the lengths of the sides, such that: [tex]2p={\ell}_1+{\ell}_2+{\ell}_3[/tex], in which [tex]p[/tex] is the semiperimeter.
Given that the perimeter of such triangle is equal to [tex]155~\text{in}[/tex] and the longest side is [tex]14~\text{in}[/tex] longer than both the other sides, we have that:
[tex]\begin{cases}{\ell}_2={\ell}_3\\ {\ell}_1+{\ell}_2+{\ell}_3=155\\ {\ell}_1={\ell}_2+14\\\end{cases}[/tex]
Using these informations, in terms of [tex]{\ell}_2[/tex], we get:
[tex]{\ell}_2+14+{\ell}_2+{\ell}_2=155[/tex]
Sum the equal terms on the left hand side of the equation
[tex]3\,{\ell}_2+14=155[/tex]
Subtract [tex]14[/tex] on both sides of the equation
[tex]3\,{\ell}_2=141[/tex]
Divide both sides of the equation by a factor of [tex]3[/tex]
[tex]{\ell}_2=47~\text{in}[/tex]
Substituting this value on the first and second equations, we get:
[tex]{\ell}_3=47~\text{in}\\\\\\ {\ell}_1=47+14=61~\text{in}[/tex]
Thus, the length of the sides of this triangle are, respectively from the largest to the smallest: [tex]{\ell}_1=61~\text{in},~{\ell}_2=47~\text{in},~{\ell}_3=47~\text{in}~~\checkmark[/tex]
These are the values we were searching for.
Mai runs 3 laps around the track in 4 minutes.
a. How many minutes per lap is that?
b. How many laps per minute is that?
C. . If Mai runs 21 laps at the
same rate, how long does it
take her?
Explain your reasoning
The total distance Mai runs is 400(4), so the distance equals 1,600 meters. If it takes her 250 meters per minutes, then if you divide 250 with 1600– it’ll take her 6.4 minutes
A car can drive 415 miles on 10 gallons of gasoline. What is the car’s mileage for 1 gallon of gas?
Answer:
41.5
Step-by-step explanation:
Answer:
41.5 miles per gallon
Step-by-step explanation:
Since you are finding the miles per gallon, you should do 415 and 10 both divided by 10 to find the number of miles for one gallon. 415 divided by 10 is 41.5, while 10 divided by 10 is 1, so for one gallon, the car can drive 41.5 miles, or 41.5 miles per gallon.
Which equations are true? Select all that apply.
A.
66
÷
10
1
=
6
.
6
66
÷
10
1
=
6
.
6
B.
660
÷
10
0
=
66
660
÷
10
0
=
66
C.
6
,
600
÷
1
,
000
=
0
.
66
6
,
600
÷
1
,
000
=
0
.
66
D.
0
.
66
÷
10
1
=
0
.
066
0
.
66
÷
10
1
=
0
.
066
E.
6
÷
100
=
0
.
06
Answer:
B
Step-by-step explanation:
If you like my answer than please mark me brainliest ty <3
There are eight more girls than boys in a school play the ratio of boys to girls is 5 to 7 how many boys and how many girls are in
the play
Answer:
This means that there are 8 more girls than boys in the school play. Hi Danielle. The ratio of boys to girls is 5:7. 5 + 7 = 12 5/12 of the students are boys.
Step-by-step explanation:
What is your favorite color?
Whoever answers first get marked brainly!!
100 piont!!!
Answer:
Blue
Step-by-step explanation:
Answer: green, I love hunter green
Step-by-step explanation:
Marketing Addis prepares marketing plans for growing businesses. For 2017, budgeted revenues are $1,500,000 based on 500 marketing plans at an average rate per plan of $3,000. The company would like to achieve a margin of safety percentage of at least 45%. The company’s current fixed costs are $400,000 and variable costs average $2,000 per marketing plan. Which of the following changes would help Marketing Docs achieve its desired margin of safety? a) The average revenue per customer increases to $4,000. b) The planned number of marketing plans prepared increases by 5%. c) Marketing Addis purchases new software that results in a 5% increase to fixed costs but reduces variable costs by 10% per marketing plan.
Answer:
1. Break even points = 400 units
margin of safety = $100
Explanation:
Given data:
budget revenue in 2017 = $1,500,000
Fixed cost =$400,000
total marketing plan = 500
take contribution margin/unit = Revenue - variable cost
= 3000 - 2000
contribution margin/unit = $1000
take break even sales $400
break even point
Break even point
margin of safety is calculated as
margin of safety = total quantity to be sold - break even sales
= 500 - 400 = $100
2. A.
(1)
Break even in marketing plan = 400
(2) Break-even in dollars:
= Break-even in marketing plan × Average rate per plan
= 400 × 3,000
= 1,200,000
(3) Margin of safety = Actual sales - Break-even sales in dollars
= 1,500,000 - 1,200,000
= 300,000
= 20%
B.
(1) Contribution margin per marketing plan = Sales - Variable cost
= $4,000 - $2,000
= $2,000
Break even in marketing plan = 200
(2) Break-even in dollars:
= Break-even in marketing plan × Average rate per plan
= 200 × 4,000
= 800,000
(3) Margin of safety = Actual sales - Break-even sales in dollars
= 1,500,000 - 800,000
= 700,000
= 47%
Therefore, option (a) would achieve the margin of safety ratio more than 45%.
Step-by-step explanation:
Zeke and his friends are heading to Light Storm Laser Tag. They plan to purchase the Light Storm group package, which will be $132 for 12 people. That's $4 less per person than the normal cost for a single player. What is the normal cost for a single player?
Answer:
15$
Step-by-step explanation:
brainliest pls
$15 is the normal cost for a single player.
Given that a game costs $132 for 12 people. That's $4 less per person than the normal cost for a single player.
We need to find the normal cost for a single player,
Let's denote the normal cost for a single player as "x" dollars.
According to the information given, the Light Storm group package costs $132 for 12 people, which means each person in the group pays $132 / 12 = $11.
We also know that the group package cost per person is $4 less than the normal cost for a single player. So, we can set up the following equation:
x - 4 = 11
Solving for "x":
x = 11 + 4
x = 15
Therefore, the normal cost for a single player is $15.
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Acrylic bone cement is sometimes used in hip and knee replacements to secure an artificial joint in place. The force required to break an acrylic bone cement bond was measured for seven specimens, and the resulting mean and standard deviation were 306.07 newtons and 41.96 newtons, respectively. Assuming that it is reasonable to believe that breaking force has a distribution that is approximately normal, use a 95% confidence interval to estimate the mean breaking force for acrylic bone cement. (Round your answers to three decimal places.)
The required 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.
Find the critical value (t*) for a 95% confidence level and (n - 1) degrees of freedom.
The degrees of freedom (df) is equal to the sample size minus 1 (df = 7 - 1 = 6). From a t-table or statistical software, the critical value for a 95% confidence level and df = 6 is approximately 2.447.
Calculate the standard error of the mean (SE).
The standard error of the mean is given by SE = (sample standard deviation) / sqrt(sample size).
[tex]SE =\dfrac{41.96}{\sqrt{7}}[/tex]
≈ 15.85
Calculate the margin of error (MoE).
The margin of error is MoE = (t*) * SE.
MoE ≈ 2.447 * 15.85
≈ 38.78
Calculate the confidence interval.
The confidence interval is given by: Mean ± MoE.
Mean ± MoE ≈ 306.07 ± 38.78
Calculate the lower and upper bounds of the confidence interval.
Lower bound ≈ 306.07 - 38.78
= 267.29
Upper bound ≈ 306.07 + 38.78
= 344.85
Therefore, the 95% confidence interval for the mean breaking force of acrylic bone cement is approximately 267.29 to 344.85 newtons.
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8. A = 84 in?
height = 4.2 in
Answer:
35 inches
Step-by-step explanation:
trough subtitution method and destributive equation
giving brain for correct answer pause.
[tex] \rm16 < x + 9 \: \: or \: \: 18 \leqslant x + 9 \\ \rm x + 9 > 16 \: \: or \: \: x + 9 \geqslant 18 \\ \rm x > 16 - 9 \: \: or \: \: x \geqslant 18 - 9 \\ \rm x > 7 \: \: or \: \: x \geqslant 9 \\ \rm \boxed{ \bold{7 < x \: \: or \: \: 9 \leqslant x}}[/tex]
help me plz asap!! !!!
Answer:
x=3
y=18
Step-by-step explanation:
Triangle CHR = Triangle KYD
Therefore:
Side CH = Side KY
<C = <K
2x+6= 12
2x=6
x=3
10x+y=48
10(3)+y =48
30+y=48
y=18
2.903 = y + 7/10 decimal in a box
Answer:
2203/1000
Step-by-step explanation:
Answer:
2.203
Step-by-step explanation:
Subtract 7/10 from both sides of the equation
2.903 = [tex]y[/tex] + 7/10
2.903 - 7/10 = y + 7/10 - 7/10
SimplifySubtract the numbers
2.903 - 7/10 = y + 7/10 -7/10
2.903 = y + 7/10 - 7/10
Subtract the numbers
2.903 = y + 7/10 - 7/10
2.903 = y
Move the variable to the left
2.903 = y
y = 2.903
plsss help 98 point pls no links
Answer:
C: individual vs individual
Step-by-step explanation:
Answer:
individual vs. society
Step-by-step explanation:
the part that says "he considers war to be of beastly madness" gives the hint
You have been gotten a job offer and the company wants to start you out at
$45,000 and will give you a 5% raise every year. Write an equation you could use to
determine how much you would be making after x number of years.
The equation that we would be making after x number of years is S(x) = 45000(1.05)^x where S(x) is the salary in xth year since the year of joining the job.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Let the initial income be P
Let the raise be of R% annually.
Then, after 1 year, it would become
[tex]P_1 = P + (R\% \: of \: P) =P + \dfrac{P}{100} \times R = P\left(1 + \dfrac{R}{100}\right)[/tex]
Now, after 1 more year(second year), we get:
[tex]P_2 = P_1\left(1 + \dfrac{R}{100}\right) = P\left(1 + \dfrac{R}{100}\right)\left(1 + \dfrac{R}{100}\right) = P\left(1 + \dfrac{R}{100}\right)^2[/tex]
After one more year(third year), we get:
[tex]P_3 = P_2\left(1 + \dfrac{R}{100}\right) = P_1\left(1 + \dfrac{R}{100}\right)^2 = P\left(1 + \dfrac{R}{100}\right)^3[/tex]
Similarly, on xth year, we get:
[tex]P_x = P\left(1 + \dfrac{R}{100}\right)^x[/tex]
This is the salary on xth year.
For this case, we're provided that:
P = $45,000R = 5Thus, we get:
[tex]P_x = P\left(1 + \dfrac{R}{100}\right)^x\\\\P_x = 45000(1 + 0.05)^x = 45000(1.05)^x = S(x) \: \rm (say)[/tex]
Thus, the equation that we would be making after x number of years is [tex]S(x) = 45000(1.05)^x[/tex] where S(x) is the salary in xth year since the year of joining the job.
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Find the values of x and y. Please help
Answer:
x= 61 degrees
y= 61 degrees
Step-by-step explanation:
A triangle is equal to 180 degrees. We already know one corner is 58 degrees, and 180-58=122 remaining degrees. We also know the 2 remaining corners are equalivent, so we can do 122/2 which gives us 61 degrees for x and y. :)
Please take a look at the picture. Please write your answer with an explanation.
Answer:
Bottom left (each term in pattern X is 1/3...)
Step-by-step explanation:
If you look at the 2nd row, you will recognize that when you multiply 15 times 1/3, you will get 5, which is 1/3 of 15. You will recognize this pattern across the whole table.
After receiving a 25% discount, Sue paid $180 for
a lawnmower. What is the original price of the lawnmower before the discount?
Answer:
$240
Step-by-step explanation:
Let's say the original price was x, then the equation would be x*0.75=180, x=180/0.75, x=240
After playing the "Spin to Win" game, which has a probability of 0.25 of winning on any individual spin, Nick decides
to play "Knock down the Bottles." To win, Nick has to knock down all 3 bottles. Nick determines that the probability of
winning this game is 0.8. Nick plays "Spin to Win" twice and then plays "Knock down the Bottles" twice.
What is the probability that Nick loses both times he plays "Spin to Win" and wins both times he plays "Knock down
the Bottles"?
O 0.04
O 0.0025
O 0.0225
O 0.36
Answer:
0.36
Step-by-step explanation:
Edge 2021
Figure A and figure B are similar right triangles.
Which series of transformations could have been applied to Figure A to create Figure B?
A dilated 150% then reflected across the x-axis
B dilated 250% then reflected across the y-axis
C dilated 250% then rotated 270 degrees clockwise about the origin
D dilated 500% then rotated 90 degrees counterclockwise about the origin
Answer:
Step-by-step explanation:
The legs of A seem to be about 2 and slightly less than 2 units in length.
The legs of B seem to be about 4.5 and 4.5 units in length
4.5/2 = 2.25 or 225% increase so NONE OF THE ABOVE answer is correct.
If we ASSUME that the legs of B are supposed to reach 5 and 5 (they don't) or the legs of A are both supposed to be 1.8 (hard to say, certainly the bottom one seems to exceed that)
then the dilation would be 5 / 2 = 2.50 or 250%
Which means we have an option of B) or C) to choose from
Reflecting A across the y axis would put B in the first quadrant so NO.
Rotating A 270° CW about the origin would give us B in the third quadrant which is correct.
So the CLOSEST answer is option C) (dilation not with standing)
Please look at the picture for question.
Answer:
A and C
Step-by-step explanation:
if u plug 3 in A and C you'll get a true eqn.
what is the slope of the line of y=2x-100
Dakota paid $301.32 for a new game system, after tax, and the tax rate is 8%. What was the original price of the game system?
Answer: 279.
Step-by-step explanation:
First, change the percentage to a decimal and write the equivalence of the sales tax amount. Let x be the original cost of the item.
Sales tax amount =x⋅0.08
Next, substitute the value into the equation:
Original Cost + Sales Tax Amount = Total Cost
x+0.08x=301.32
Add like terms.
1.08x=301.32
Divide both sides by 1.08 to isolate the unknown value.
x=$279
You are running a fuel economy study. One of the cars you find is blue. It can travel 45 1/2 miles on 1 1/4 of gasoline. Another car is red. It can travel 23 3/5 miles on 4/5 of gasoline. What is the unit rate for miles per gallon for each car? Which car could travel the greater distance on 1 gallon of gasoline?
9514 1404 393
Answer:
blue: 36.4 mpgred: 29.5 mpgblue goes farther on 1 gallonStep-by-step explanation:
You find miles per gallon by dividing miles by gallons. ("Per" essentially means "divided by.")
blue(45.5 mi)/(1.25 gal) = 36.4 mpg
red(23.6 mi)/(0.8 gal) = 29.5 mpg
__
"Miles per gallon" is the number of miles traveled on one gallon. The blue car can travel a greater distance on 1 gallon of gasoline.
Gabriel is constructing a triangle's two sides and the measure of the angle between them. Which choice shows the step
in which Gabriel discovers information that was not given about the triangle?
Answer:
i dont know what to tell u man that hard
Step-by-step explanation:
Evaluate. (15+12)2+310⋅5 Enter your answer as a mixed number in simplest form by filling in the boxes. $$
Hey there!
(15+12)(2)+ 310(5)
= 27(2) + 310(5)
= 54 + 1,550
= 1,604
Therefore, your answer is should be: 1,604
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Answer: THE CORRECT ANSWER IS 125/64
NOT 1/4
The graph of a function f is shown below. For how many values of x is f(x)=−4? WORTH A LOT
9514 1404 393
Answer:
4 values
Step-by-step explanation:
Draw a horizontal line at y = -4. Count how many places it crosses the graph.
There are 4 values of x where f(x) = -4.
A line passes through the points(-8,-7) and (-4, -4) what is the equation of the line in slope intercept form
Step-by-step explanation:
(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)
(y + 7)/(-4 + 7) = (x + 8)/(-4 + 8)
(y + 7)/3 = (x + 8)/4
4(y + 7) = 3(x + 8)
4y + 28 = 3x + 24
4y = 3x + 24 - 28
4y = 3x - 4
y = 3x/4 - 1
Find an equation with a solution of x=6 of multiplicity 1, and a solution of x= 3 of multiplicity 2.
Write your answer in standard form.
A friend tells you that her savings account doubled in 6 years. Use the Rule of 72 to estimate what the APR of her account was.
Answer:
12
Step-by-step explanation:
Just divide 6 into 72 to find that it will require an interest rate of about 12 percent.
Hannah wants to buy cupcakes and cookies for her friends with a budget of $35. Cupcakes are $6
and cookies are $1.
1. What is the maximum amount of
cupcakes she can buy?
2. if she buys the maxium amount of cupcakes, how many cookies will she be able to buy?
1. Since Hannah cannot buy a fraction of a cupcake, the maximum number of cupcakes she can buy is 5.
2. If Hannah buys the maximum amount of cupcakes (5 cupcakes), she will be able to buy 5 cookies with the remaining budget.
To find the maximum number of cupcakes Hannah can buy, we need to divide her budget by the cost of each cupcake:
1. Maximum cupcakes she can buy:
Maximum cupcakes = Budget / Cost per cupcake
Maximum cupcakes = $35 / $6 ≈ 5.83 (rounded down to the nearest whole number, as you cannot buy a fraction of a cupcake)
Since Hannah cannot buy a fraction of a cupcake, the maximum number of cupcakes she can buy is 5.
2. If she buys the maximum amount of cupcakes (5 cupcakes), we can find out how many cookies she can buy with the remaining budget.
Remaining budget after buying cupcakes:
Remaining budget = Total budget - (Number of cupcakes * Cost per cupcake)
Remaining budget = $35 - (5 * $6)
Remaining budget = $35 - $30
Remaining budget = $5
Now, we can calculate the number of cookies she can buy with the remaining budget:
Number of cookies = Remaining budget / Cost per cookie
Number of cookies = $5 / $1 = 5
Hence, if Hannah buys the maximum amount of cupcakes (5 cupcakes), she will be able to buy 5 cookies with the remaining budget.
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