Answer:
Sister = 15 years old
Brother = 12 years old
Step-by-step explanation:
Right now, if the brother is B years old and the sister is S years old, B = (4/5)S because the ratio from brother to sister is 4:5, so if one unit is X, B = 4X and S = 5X
Three years ago, the brother was B-3 years old and the sister was S-3 years old. Keeping one unit as X, we have
B = 3X
S = 4X
B-3 = (3/4)(S-3)
Therefore, we have a system of equations
B = (4/5)S
B-3 = (3/4)(S-3)
Substitute (4/5)S for B into the second equation to only have one variable
(4/5)S - 3 = (3/4)(S-3)
(4/5)S - 3 = (3/4)S - 9/4
add 3 to both sides and subtract (3/4)S from both sides to isolate the variable and its coefficient
(1/20)S = 3/4
multiply both sides by 20 to isolate the S
S = 15
B = (4/5)S = 12
I need helpBarbara works at a law office as an entry level lawyer. She spends 2/5 of her time at the law office doing paper work. How many hours does she have to work to spend 10 hours doing paper work.
GIVEN:
We are told that Barbara works 2/5 of her time doing paper work and this fraction represents 10 hours of her total working time.
Required;
To determine how many hours she will have to work in order to have 10 hours doing paper work.
Step-by-step solution.
Take note that her entire working hours is represented by 1 whole since, a fraction of it has already been identified as two-fifths.
This means
\(\frac{2}{5}\times h=10\)Take note that the fraction is taken as two-fifths of the total hours h and, if multiplied by the total hours, we would get 10 hours.
Hence, if we simplify the above equation, we would get the value of h as follows;
\(\begin{gathered} \frac{2}{5}\times h=10 \\ \\ Cross\text{ }multiply: \\ \\ h=\frac{10\times5}{2} \\ \\ h=25 \end{gathered}\)Therefore,
ANSWER:
Barbara has to work for 25 hours in order to spend 10 hours on paper work.
Please help ASAP, I need to answer this by the end of the day I need really need help!!!
Answer:
1. I believe some solutions could be x= -7, x= -8, x= -9 etc.
Step-by-step explanation:
2. If the inequality was -3x is greater than or equal to 18 then x and also be equal to x=6.
PLEASE HELP!
Which graph represents f(x) = 1/2x^5
The solution is option a)
How to graph an equation?
To graph an equation using the slope and y-intercept. Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). Next, plot the y-intercept. From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
Given data ,
Let the function be f ( x ) = ( 1 / 2 ) x⁵
Now , to know which graph represents the equation mentioned, you can put some values of x in the equation and evaluate the value of y
So , when x = 1
y = ( 1 / 2 )
when x = 2
y = ( 1 / 2 ) × 2⁵
= 2⁴
= 16
when x = -1
y= ( 1 / 2 ) × ( -1 )⁵
= - ( 1 / 2 )
So , by plotting all the points of x and y in the graph , Option a ) satisfies the solution
Hence , the solution is Option a)
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4. Maliyah has 3 54 cups of dough for baking bread. Each loaf of bread requires96 of a cup of dough. What is the exact number of loaves that Maliyah canmake from the dough?
Write 3 3/4 as a fraction:
\(3\frac{3}{4}=3+\frac{3}{4}=\frac{12}{4}+\frac{3}{4}=\frac{15}{4}\)Use conversion factor to find the exact number of loaves that Maliyah can make with 3 3/4 (15/4) cups of dough.
1 loaf requires 1/6 of cup of dough.
\(\frac{15}{4}\text{cups}\cdot\frac{1\text{loaf}}{\frac{1}{6}\text{cup}}=\frac{15}{4}\text{cups}\cdot6\frac{\text{loaf}}{\text{cup}}=\frac{90}{4}\text{loaves}=\frac{45}{2}\text{loaves}\)You can write the answer as a mixed number:
\(\frac{45}{2}=\frac{44}{2}+\frac{1}{2}=22\frac{1}{2}\)Then, with 3 3/4 cups of dough Maliyah can make 22 1/2 (45/2) loaves of bread.
Describe two ways to find the distance between two points in a
coordinate plane.
find the area of the equilateral triangle
Answer:
3.90 sq cm
Step-by-step explanation:
\(A_{equilateral\: \triangle} = \frac{ \sqrt{3} }{4} \times {(side)}^{2} \\ \\ = \frac{ \sqrt{3} }{4} \times {(3)}^{2} \\ \\ = \frac{9 \sqrt{3} }{4} \\ \\ = 3.89711432 \: {cm}^{2} \\ \\ \approx \: 3.90 \: {cm}^{2} \)
The art club is designing a rectangular mural for the school hallway. Three corners are located in a coordinate plane at the following locations: (–1, –1), (–1, 1), and (4, 1).
What is the ordered pair for the fourth corner?
Answer:
That fourth ordered pair is (4, -1)
Step-by-step explanation:
A rectangle is a set of permutations of x and y
x can either be -1, or 4
y can either be -1, or 1
the only one missing from this set is (4, -1)
F(x) = 3x + 1 and f^-1=x-1/3
then f(2)
Input:
{F(x) = 3 x + 1, 1/f = x - 1/3 f(2)}
Result:
{F(x) = 3 x + 1, 1/f = x - f(2)/3}
Alternate forms:
{3 x + 1 = F(x), 3 x = f(2) + 3/f}
{F(x) = 3 x + 1, f(2) = 3 x - 3/f}
{F(x) = 3 x + 1, 1/f = 1/3 (3 x - f(2))}
Alternate form assuming f and x are positive:
{3 x + 1 = F(x), 3 f x = f(2) f + 3}
is this correct?
if not does anybody know which one it is
Answer:
hey, i just did this question and double checked everything and i got a different answer.
So C, =x^2−25 should be the correct one
Step-by-step explanation:
good luck on the test
Please help !! Write a sequence of rigid transformations that could take one triangle to another
The required scale factor of the dilation, between the triangles, is 3/4.2.
What is the transformation of geometry over the coordinate plane?Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.
Here,
To determine, a sequence of rigid transformations that could take one triangle to another.
Since as we can see, the triangles have certain dilation, translation, and reflection. As for the data given, we can only calculate the dilation factor or scale factor only.
So,
Scale factor = Length of the one side of 1st triangle/length of 2nd triangle.
Scale factor = 6/8.4
Scale factor = 3/4.2
Thus, the required scale factor of the dilation, between the triangles is 3/4.2.
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What is the volume of the rectangular prism?
Height : 10 1/2 in.
Width : 2 3/4 in.
Length : 5 in.
Answer:
Step-by-step explanation:
volume=10 1/2 ×2 3/4 ×5
=21/2×11/4×5=1155/8=144 3/8 cubic inch
What is the highest common factor of 30 and 132?
Answer:
6
Step-by-step explanation:
hope this helps
Lily and nada share silver coins in the ratio 7:3. if lily gives 3 silver coins to nada, the ratio becomes 5:3. how many silver coins did lily have initially?
The number of silver coins Lily initially had is 28.
What is ratios?A ratio is described as a comparing two quantities with the same unit to determine the amount of each quantity is existent in the other. Ratios are divided into two types.
The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groups.Now according to the question;
Let 'x' be the share of silver coin of Lily.
Let 'y' be the share of silver coin of Nada.
Lily and Nada share silver coins in the ratio 7:3
Thus, x/y = 7/3
Cross-multiplying
3x = 7y (equation 1)
Now, if Lily gives 3 silver coins to Nada, the ratio becomes 5:3.
(x - 3)/(y + 3) = 5/3
cross multiplying;
3x - 9 = 5y + 15
Simplifying;
3x = 5y + 24 (equation 2)
Comparing equation 1 and 2.
7y = 5y + 24
2y = 24
y = 12 (Nada's share)
Substitute the value of y in equation 1;
3x = 7y
3x = 7×12
x = 28
Therefore, the initial share if Lily was 28.
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in a survey conducted on an srs of 200 american adults, 72% of them said they believed in aliens. give a 95% confidence interval for percent of american adults who believe in aliens.
American adults believes in alien for the given 95% confidence interval and sample surveyed is in the interval range of ( 0.66 , 0.78 ).
As given in the question,
Sample of American adults surveyed 'n' = 200
Percent of people believes in aliens are success 'p'= 72%
= 0.72
Percent of people who don't believes (failure) in aliens ' 1 - p' = 1 - 0.72
= 0.28
95% Confidence interval that represents Americans adults who believes in aliens
value of z - score for 95% confidence interval = ± 1.96
Margin of error 'MOE'= (z-score)√p ( 1- p) /n
= ( 1.96)√(0.72 × ( 1 - 0.72 )/ 200
= 1.96 ( √0.2016 / 200)
= 1.96 ×√0.001008
= 0.063
Lower limit = p - MOE
= 0.72 - 0.063
= 0.66
Upper limit = p + Margin of error
= 0.72 + 0.063
= 0.78
Therefore, 95% confidence interval with sample size of the Americans adults who believes in alien are in the interval of ( 0.66 , 0.78 ).
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Margo walks to her friend's house in 10 minutes. Using the same route, it takes Margo 20 minutes to get back home. If her average walking rate for the entire trip is 4 miles per hour, how many total miles did she walk?
Answer:
Margo walks 1 mile
Step-by-step explanation:
Given that;
Margo walks to her friend's house in 10 minutes.
Using the same route, it takes Margo 20 minutes to get back home.
Total walking rate = 20+ 10 = 30 minutes
The average of her walking rate for the entire trip is 4 miles per hour
i.e 30/2 minutes = 4 miles/hr
15 minutes = 4 miles/hr
Let x be the total number of miles that Margo walk;
So;
15 minutes × x = 4 miles/hr
15 minutes × x = 4 miles/ 60 minutes
x = (4 miles/ 60 minutes) × 15 minutes
x = 1 mile
Thus, Margo walks 1 mile
Answer:
Margo walks 1 mile
Step-by-step explanation:
Nina owns a condominium where she paid $3,340 in maintenance fees this year. If her property taxes are 15% of this amount, how much did Nina pay in property taxes?
Nina pay in property taxes 501. or \(5.01*10^{2}\).
A property tax, often known as a millage rate, is an ad valorem tax based on a property's value. The tax is imposed by the administrative body of the region where the property is situated. This could be the federal government, a federated state, a county, a region of land, or a municipality. The average effective property tax rate in the Lone Star State is 1.60%, making Texas' property taxes the seventh-highest in the nation. Comparing that to the current 0.99% national average will help. Property taxes in Texas cost the average homeowner $3,797 a year. It is well known that British property owners do not pay property tax. But hold on, it's too soon to celebrate because there might still be taxes to pay.
Based on the given conditions, formulate:
3340*15%
Calculate.
501
Alternative forms.
\(5.01*10^{2}\)
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what is 500 X 500X 2
Answer:
Input:
500×500×2
Result:
500000
Step-by-step explanation:
here is how i got the answer
500000
SOLUTION STEPS :
500⋅500⋅2= Multiply 500 and 500 to get 250000. 250000×2 Multiply 250000 and 2 to get 500000. 500000 FACTOR2 ^5 × 5^6 Which equals 500000.
________________________________________________________
hope this helps, let me know if i am wrong, and Brainliest?
please help! provide step by step, clear explaination! algebra 1 work. thanks
In a triangle ABC, a= 4 cm, b= 5 cm, c = 3 cm. Find the area of the triangle.
The area of the triangle ABC is 6 square centimeters.
To find the area of the triangle, we can use Heron's formula, which is based on the lengths of the triangle's sides. Heron's formula states that the area (A) of a triangle with side lengths a, b, and c can be calculated using the following formula:
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the side lengths are given as a = 4 cm, b = 5 cm, and c = 3 cm.
Calculating the semi-perimeter:
s = (4 + 5 + 3) / 2 = 6 cm
Using Heron's formula:
A = √(6(6-4)(6-5)(6-3))
= √(621*3)
= √(36)
= 6 cm²
Therefore, the area of triangle ABC is 6 square centimeters.
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Currently learning surface area, and I have a test tomorrow. I don’t understand it AT ALL. Need help, ASAP!
(Many of the answers on this paper are wrong)
Answer:
2 triangles + 3 different rectangles = total surface of the triangular prism
Step-by-Step:
Honestly, the best way I can help you is to give you a proper way but you must know how to find each area on each shape of the triangular prism.
First, Calculate each Triangle by its area.
1/2 times base times height = surface area of triangle
Then, Calculate each Rectangle by its area.
base times height = surface area of rectangle
Once you have each area of the shape of the prism, you add all of them to get the total surface area.
2 triangles + 3 different rectangles = total surface of the triangular prism
what is a hypothesis? what is the null hypothesis? what is the alternate hypothesis? how is reasonable doubt raised about a null hypothesis? what is a p-value? after analyzing a set of data, if the results support a hypothesis, does that prove the hypothesis is true? explain. after analyzing a set of data, if the results are inconsistent with a hypothesis, does that prove the hypothesis is false? explain. briefly describe the reasoning of hypothesis testing. explain the difference between a two-sided alternative hypothesis and a one-sided alternative hypothesis. which test is more conservative, a one-sided or two-sided test? how do we measure the size of the effect when we test a hypothesis?
A hypothesis is an educated guess about a phenomenon that can be tested through experimentation or observation. The null hypothesis is the hypothesis that nothing is happening, and the alternative hypothesis is the hypothesis that there is an effect or difference. Reasonable doubt about a null hypothesis can be raised by finding evidence that contradicts it. A p-value is the probability that the results obtained in a study or experiment occurred by chance alone.
After analyzing a set of data, if the results support a hypothesis, this does not prove the hypothesis is true. This means the hypothesis is consistent with the data but further evidence or experimentation must be done to truly prove the hypothesis. After analyzing a set of data, if the results are inconsistent with a hypothesis, this does not prove the hypothesis is false. It could be due to chance or an inadequately tested hypothesis.
The reasoning of hypothesis testing is to determine if the results of a study or experiment support the null hypothesis or alternative hypothesis. A two-sided alternative hypothesis is when the difference between two groups is tested to be either greater or lesser than the reference value, whereas a one-sided alternative hypothesis tests the difference to be only greater or lesser than the reference value. A one-sided test is more conservative than a two-sided test as the former has a higher risk of making a type II error. The size of the effect when testing a hypothesis can be measured by the power of the test and the magnitude of the effect.
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What is the solution to the inequality 3a/2 < 24
Answer:
a < 16
Step-by-step explanation:
We must get a alone to solve this. So first multiply by 2
3a/2 < 24
*2
3a < 48
Divide by 3
a < 16
Match the numbers with the correct label.
how are we suposed to do this
How many solutions does the following equation have?
53 +8 – 7x = -4x +1
=
Choose 1 answer:
А
No solutions
B
Exactly one solution
С
Infinitely many solutions
Answer:
One solution
Step-by-step explanation:
So long as you don't have any term x² or to a power higher than 2, the equation will have 1 solution only.
There are 12 rabbits at a pet store Gabriela has 5 1/2 ounces of parsley to feed the rabbits how much parsley does each rabbit get???
Answer:
2.18 ounces
Step-by-step explanation:
12/5.5=2.181...
rounded it is 2.18
hope this helps :3
if it did pls mark brainliest
first one that gets it correctly gets branlyest
Answer:
200 in2
Step-by-step explanation:
diameter= 15 in. so raduis = 15/2
area of circle = πr2
= 22/7 * 15/2 *15/2
= 176.79
rounding to the nearest 100, its 200 in2
It costs $0.40 per mile to ride the train from Minneapolis to Duluth, Minnesota. If the entire trip costs $54.80, what is the distance from Minneapolis to Duluth?
Answer:
the distance from Minneapolis to Duluth is 137 miles
Step-by-step explanation:
The computation of the distance from Minneapolis to Duluth is shown below:
Given that
The cost per mile is $0.40
And, the total trip cost is $54.80
So based on the above information
The distance from Minneapolis to Duluth is
= $54.80 ÷ $0.40
= 137 miles
Hence, the distance from Minneapolis to Duluth is 137 miles
The same would be considered
Find two numbers having a difference of 16 such that the result of adding their sum and their product is a minimum
Answer:
-8.5 and 7.5
Step-by-step explanation:
Let's call the two numbers x and y. We know that their difference is 16, so we can write:
x - y = 16 or x = y + 16
We want to find the values of x and y that minimize the expression:
x + y + xy
Substituting x = y + 16, we get:
(y + 16) + y + (y + 16)y
Simplifying and expanding, we get:
y^2 + 17y + 16
To minimize this expression, we can take its derivative with respect to y and set it equal to 0:
d/dy (y^2 + 17y + 16) = 2y + 17 = 0
Solving for y, we get:
y = -8.5
Substituting y = -8.5 into x = y + 16, we get:
x = 7.5
Therefore, the two numbers with a difference of 16 such that the result of adding their sum and their product is a minimum are -8.5 and 7.5.
A book cost $18 that is 3 times more than a dvd how much does a dvd cost
Answer:
Hi! This question tells us that the book costs $18 and that it costs 3 times more than a DVD. In order to determine the cost of the DVD, all we have to do is divide 18 by 3. 18 divided by 3 is 6. Therefore, the DVD costs $6.
Hope this helps!
Answer:$6
Step-by-step explanation: 18÷3=6
Given the two rectangles below. Find the area of the shaded region.
7
2
4
2
Answer:
\text{ units}^2 units
2
Answer:
52 units²
Step-by-step explanation:
A = L × W
Area = Length × Width
First find the total area: 44
Half that to find the total left side that is shaded: 22
Find the bottom right side, imagine it is a seperate shape. It would be 4 × 2 = 8. 44 + 8 = 52.
- Educator