107/56 is the solution of fractions .
What do math fractions mean?
An element of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.The given fractions are 5/8 and 1 2/7.
We need to find the sum of given fractions.
Now, we can write 1 2/7 as 9/7.
So, 5/8 + 9/7
Here, LCM of 8 and 7 is 56
Then, 35/56 + 72/56
=(35+72)/56
=107/56
Therefore, the sum of the two given fractions is 107/56.
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after two years $900 deposited in a savings account with simple interest had earned $18 in interest. what was the interest rate
The expression for Simple Interest is :
[tex]\text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100}[/tex]Given that Principal amount = $900
Time period = 2 years
Simple Interest = $18
Substitute the value and solve for RAte of interest
[tex]\begin{gathered} \text{Simple Interest = }\frac{\text{ Principal AMount}\times Time\text{ }\times Rate\text{ of Interest}}{100} \\ 18=\frac{900\times2\times R}{100} \\ R=\frac{18\times100}{900\times2} \\ R=1 \\ \text{ Rate of interest = 1 percent} \end{gathered}[/tex]Answer : Interest Rate = 1%
Helen borrowed $2,500 for home repairs. She paid back 24 payments of$115 each. How much did she pay in interest on the loan?a. $108.96b. $4.79c. $2,760d. $260
To solve this problem, we will compute the total amount Helen paid back and we will subtract $2,500 from it.
To determine the total amount she paid back we multiply the number of payments by the amount of each payment:
[tex]T=24\times115\text{dollars}=2760\text{ dollars.}[/tex]Subtracting $2,500 from the above result we get:
[tex]2760-2500=260\text{dollars.}[/tex]Answer: Option d.
In general, the value of a car decreases with age. Provide an estimate that could show the correlation between the age and value of a car. Provide numerical response rounded to the nearest tenths
Answer:
in general, the value of a car decreases with age what would ne the correlation between the age and values of all cars -1, 0.7, 1, -0.7
What is the greatest common factor of this expression?
12m + 18m2
A.
2m
B.
6m
C.
6
D.
2
Answer:
I think the answer is B because when you check the factors, you get 6 then you add your unit
Lena prepared 4.3 kilograms of dough after working 2 hours. How many hours did Lena work if she prepared 10.75 kilograms of dough? Assume the relationship is directly proportional.
Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 directly proportional 2.
What is proportional?A comparison of two numbers mathematically is called a proportion. Two sets of given numbers are said to be directly proportional to one another if they increase or decrease in the same ratio, according to the law of proportion. The symbols "::" or "=" are used to indicate proportions.
We have given that 4.3 ∝ 2
where 4.3 kilograms is completed in 2 hours
If 4.3 ∝ 2, the constant k is
4.3 = k2
k = 4.3/2
k = 2.15
We have asked to find how many hours did Lena work if she prepared 10.75 kilograms of dough.
Let hours she took be x, Thus
10.75 ∝ x
We already have the contestant, so this gives us
10.75 = kx
10.75 = 2.15x
x = 10.75/2.15
x = 5 hours
Thus, Lena worked for 5 hours if she prepared 10.75 kilograms of dough assuming 4.3 ∝ 2.
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A firecracker sends a small pebble vertically upward from a height of 35 feet above a
pool of water. The starting speed of the pebble is 85 feet per second. Its distance in
feet, d, above the water is given by the equation:
d=35+85t-16t2, where t is the time in seconds after the launch.
Drag statements to the table to show what each coordinate labeled on the graph
represents in this problem situation.
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included.It also goes by the name quadratic equations.The quadratic equation has the general form ax2 + bx + c = 0.where a, b, and c are numerical coefficients and x is an unknown variable.
Solve the quadratic equation?
d=35+85t-16t²
35+85-16t²-d
35+85t-16t²-d=0
35-d+85t-d=0
16t²-85t-35+d=0
t=85±√[tex]\sqrt{x}[/tex]-(85)²-4×16(-35+d)/2×16
t=85±√(-85)²-4×16(-35+d)/32
-(85)²-4×16(-35+d)
=7225-64(-35+d)
=7225-64(-35+d)
7225+2240-64d
=9465-64d
=-9401
t=85+√9465-64d/32
t=85+97
t = 182
t=85-√9465-64d/32
t=85-97
t = -12
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tern US po.. Performance Matte... Student: Login Students and Famili... ReadWorks C Clever | Portal Madison White - Su... https://usea for School: Additional Practice 1.6.AP-24 Question Help 1 Marta has 31- ft of tape to be used for taping up boxes. Complete parts a and b. 4 2 got your answer. IL 1 1 125 25 125 2. 1 31= = 12 х 4 2 4 2 4. 25 = 22 (Type whole numbers, fractions, or mixed numbers.) So, Marta can tape boxes with (Type whole numbers, fractions, or mixed numbers.) boxes with ft of tape left over. H More Enter your answer in the edit fields and then click Check Answer. 1 part Clear All Check Ans remaining
Martha has 31 1/4 ft of tape to be used for taping up boxes
Each box needs 12 1/2 ft of tape
To find how many boxes Martha can tape up, we need to divide 31 1/4 by 12 1/2
First, we need to convert these mixed numbers into fractions, as follows:
[tex]\begin{gathered} 31\frac{1}{4}=\frac{31\cdot4+1}{4}=\frac{125}{4} \\ 12\frac{1}{2}=\frac{12\cdot2+1}{2}=\frac{25}{2} \end{gathered}[/tex]Dividing by a fraction is the same as multiplying by its inverse, then:
[tex]\frac{31\frac{1}{4}}{21\frac{1}{2}}=\frac{\frac{125}{4}}{\frac{25}{2}}=\frac{125}{4}\cdot\frac{2}{25}=\frac{5}{2}=2\frac{1}{2}[/tex]Given that you can't tape up 2 1/2 boxes, Martha can only tape up 2 boxes. To tape up 2 boxes she needs the next amount of tape:
[tex]12\frac{1}{2}\cdot2=\frac{25}{2}\cdot2=25\text{ ft of tape}[/tex]The leftover is computed as follows:
[tex]31\frac{1}{4}-25=6\frac{1}{4}\text{ ft of tape}[/tex]So, Martha can tape 2 boxes with 6 1/4 ft of tape left over
Graph the solution set l 2x + 4l + 2 <= 8
ANSWER :
EXPLANATION :
From the problem, we have :
[tex]\begin{gathered} \lvert{2x+4}\rvert+2\le8 \\ \text{ which can be simplified as :} \\ \lvert{2x+4}\rvert\le6 \end{gathered}[/tex]Note that in solving absolute values, the terms inside the absolute value sign can have inverse signs.
Case 1 : Positive
[tex]\begin{gathered} 2x+4\le6 \\ 2x\le2 \\ x\le\frac{2}{2} \\ \\ x\le1 \end{gathered}[/tex]Case 2 : Negative, the symbol will change since we are multiplying a negative number
[tex]\begin{gathered} -(2x+4)\ge6 \\ -2x-4\ge6 \\ -2x\ge10 \\ x\ge\frac{10}{-2} \\ \\ x\ge-5 \end{gathered}[/tex]So the solution is :
[tex]\begin{gathered} x\le1\quad and\quad x\ge-5 \\ \text{ when written together :} \\ -5\le x\le1 \end{gathered}[/tex]or in interval notation :
[-5, 1]
The graph of it will be :
5÷4=
what is the quotient
g(x) = 4x²-2 on [x, x + h] average rate of change
The average rate of change of function g(x) = 4x²-2 on [x, x + h] is 4h+8x.
What is average rate of change?The average rate at which one quantity changes in relation to another's changing is referred to as the average rate of change function. A process that computes the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.
The average rate of change of y = g(x)over an interval between 2 points (a, f(a)) and (b ,f(b)) is the slope of the secant line connecting the 2 points.
To calculate the average rate of change between the 2 points.
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
f(x + h) = 4(x+h)²-2
= 4x² + 8hx + 4h² − 2
f(x) = 4x²-2
The average rate of change between (1 ,4x²-2) and (5 ,4x² + 8hx + 4h² − 2) is
[tex]\frac{(4x^2 + 8hx + 4h^2-2) -(4x^2-2) }{(x+h)-x}[/tex]
= 4h+8x
This means that the average of the slopes of lines tangent to the graph of f(x) between (1 ,4x²-2) and (5 ,4x² + 8hx + 4h² − 2) is 4h+8x.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
its 5
Step-by-step explanation:
f
dddd
Graph the parallelogram STUV with vertices S(-3,4),T(-1 , 7), U(5, 7) and V(3, 4) on your paper then give the ordered pairs with the reflection of the line y = - x .
Graph the polygon using the coordinates of its vertices
What is the solution of the system of equations? 6x-2y = 4 -9x+3y = 12
We will have the following:
First, we solve both equations for y, that is:
[tex]6x-2y=4\Rightarrow-2y=-6x+4[/tex][tex]\Rightarrow y=3x-2[/tex]&
[tex]-9x+3y=12\Rightarrow3y=9x+12[/tex][tex]\Rightarrow y=3x+4[/tex]From this we can see that they are parallel lines, that do not share any common points, so there is no solution for the system.
Greg graduated in the bottom 9% of his class. If the mean was 585 and the standard deviation was 134, and the distribution was normal, what was Greg's raw score?
Greg's raw score in the test is 405
How to determine the raw score of the test?The given parameters are
Mean = 585Standard deviation = 134Proportion, p = bottom 9%The above implies that
z = P(p < 0.09)
From z tables of probabilities, we have
z = -1.34
The z-score of the data value is calculated using the following formula
z = (raw score - mean value)/standard deviation
Substitute the given parameters in the above equation
-1.34 = (raw score - 585)/134
This gives
-180 = raw score - 585
So, we have
raw score = 585 - 180
Evaluate
raw score = 405
Hence, the raw score is 405
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) Anita prepared 28 kilograms of
dough after working 4 hours. How
much dough did Anita prepare if she
worked for 5 hours? Solve using unit
rates.
Answer: should be around 35 kilos dont got an explaination just used meh brain
Step-by-step explanation:
help mee pleasee!!
thank you <3
The equation of the line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
In this question we have been given two points.
We need to find an equation of the line passing through points (-2, 1) and (1, -4)
Using the two-point form of equation of line.
(y - y1)/(y2 - y1) = (x - x1) / (x2 - x1)
(y - 1) / (-4 - 1) = (x - (-2)) / (1 - (-2))
(y - 1) / (-5) = (x + 2) / (1 + 3)
y - 1 / (-5) = (x + 2) / 4
y - 1 = (-5/4)(x + 2)
y = -5x/4 - 10/4 + 1
y = (-5/4)x - 3/2
Let y = f(x)
so, equation of line is f(x) = (-5/4)x - 3/2
Therefore, the equation of line passing through points (-2, 1) and (1, -4) is f(x) = (-5/4)x - 3/2
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8. In the accompanying diagram of isosceles triangle ABC, AB = BC, m
In the given Isosceles triangle,
AB = BC
Since, from the property of issoceles triangle
Angle opposite to equal sides of a triangle are always equal,
So, in the given figure
Angle Opposite to side AB is angle C
Angle Opposite to side BC is angle A
so, Angle A = Angle C
[tex]\begin{gathered} \angle A=\angle C \\ \text{ Since, it is given that }\angle A=x^{\circ} \\ So,\text{ }\angle C=\angle A=x^{\circ} \end{gathered}[/tex]The sum of all angles in a triangle is equal to 180 degrees
[tex]\begin{gathered} In\text{ triangle ABC} \\ \angle A+\angle B+\angle C=180^{\circ} \\ x^{\circ}+(x+30)^{\circ}+x^{\circ}=180^{\circ} \\ x^{\circ}+x^{\circ}+30^{\circ}+x^{\circ}=180^{\circ} \\ 3x^{\circ}+30^{\circ}=180^{\circ} \\ 3x^{\circ}=180^{\circ}-30^{\circ} \\ 3x^{\circ}=150^{\circ} \\ x^{\circ}=\frac{150^{\circ}}{3} \\ x^{\circ}=50^{\circ} \end{gathered}[/tex]Answer : b) x = 50
1:
Jerrod brought 48 cupcakes to school. At school, he gave 3 cupcakes to
each student in his class. He has 6 cupcakes remaining. How many
students are in Jerrod's class? Variable,equation and answer
Answer:
There were eight studentsin jerrods class
Greg Losier put $26,500 down on a $92,500 home.
How much did he have to mortgage?
Using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the mortgage will be:
$92,500 - $26,500Solve this expression as follows:
$92,500 - $26,500$66,000Therefore, using mathematical operations we conclude that Greg has to mortgage the amount of $66,000.
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Which of the following statements are true?
Choose all answers that apply:
The equation represents a proportional relationship.
The unit rate of change of y with respect to a is
7
2
The slope of the ne is
2
A change of 7 units in a results in a change of 2 units in y.
A change of 6 units in a results in a change of 21 units in y.
Based on the function given of y = 2.5x, the true statements are:
The equation represents a proportional relationship.The slope of the line is 2.5.A change of 2 units in x results in a change of 5 units in y.What is proportional relationship?
When two variables are correlated in a manner that their ratios are equal, this is known as a proportional relationship. In a proportional connection, one variable is always a constant value multiplied by the other, which is another way to think of them. The "constant of proportionality" is the name of this constant.The equation y = 2.5x is a proportional relationship because y increases by a certain amount when x increases. That amount is shown by the slope of the line which is 2.5.
For instance, if there is a change of 2 in x, the change in y would be:
= 2.5 × x
= 2.5 x 2
= 5
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Figure W was ___ to create W’. Figure W’ was dia lates by a scale factor of ___ fromThe origin to create w”
Transformations
One of the rigid transformations is reflection. When a figure is reflected across some line, it maps to the very same shape but inverted as if the line was a mirror.
Right between figures W and W' the y-axis separates two identical images as if the y-axis was a mirror, thus:
Figure W was reflected over the y-axis to create figure W'
A Dilation from the origin maps an object to another such that its vertices are all multiplied by a common factor (scale factor).
For example, the upper-right vertex of W' is located at (2-2). The upper-right vertex of W'' is at (4,-4). The scale factor is 2.
The bottom-left vertex of W' is at (4,-4) and the bottom-left vertex of W'' is at (8,-8). We find the same scale factor of 2. If we tested all of the vertices, we'll obtain the same scale factor of 2, thus:
Figure W' was dilated by a scale factor of 2 from the origin to create figure W''
It takes you 6 hours to row 12 miles, how long will it take you to row 32 miles.
Answer:16
Step-by-step explanation:
1 hour=2miles
A rabbit runs 35 miles per hour. A fox can run 21 miles in half an hour. Which animal is faster, and by how much?
Answer:
The fox can run faster by a factor of 7 miles per hour
Step-by-step explanation:
If the fox runs 21 miles in half of an hour, that means that by multiplying the fraction 21miles/0.5hours by 2/2 you can find that the fox runs 42 miles per hour, 7 miles per hour faster than the rabbit.
Answer:
The Fox, by 7 Miles per hour
Step-by-step explanation:
The rabbit runs 35 Miles per hour
The Fox runs 21 in half an hour
1 hour - 30 minutes = 30 minutes meaning we have to double the foxes miles
21 x 2 = 42
42>32
To find out by how much do 42-32 and we get 7 Miles per hour.
Studying for a test, need some help solving this question
Solution
Part A
To find C
[tex]_{\angle\text{ C+}\angle A+\angle B=180^0(Sum\text{ of angles in a triangle\rparen}}[/tex][tex]\begin{gathered} \angle C+33.84+19.32=180 \\ \angle C+53.16=180 \\ \angle C=180-53.16 \\ \angle C=126.84^0 \\ \end{gathered}[/tex]Part B
To find a
Using sine rule
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex][tex]\begin{gathered} \frac{sin33.84}{a}=\frac{sin126.84}{13.95} \\ cross\text{ multiply} \\ asin126.84=13.95sin33.84 \\ divide\text{ both side by sin126.84} \\ \\ a=9.70672 \end{gathered}[/tex]Part C
To find b
Using sine rule
[tex]\begin{gathered} \frac{sin33.84}{9.70672}=\frac{sin19.32}{b} \\ \\ \\ b=5.76683 \end{gathered}[/tex]Patricia O'Malley purchased fifty $1,000 bonds having a quoted price of 99.75. She paid a 6.5% brokerage fee of the selling price). What was the total cost of the bond sale(to the nearest whole cent)?$53,116.88$54,024.65$55,346.77$58,021.99None of these choices are correct.
It is given that 50 bonds were bought with a cost of $1000 each.
6.5% brokerage was paid.
The total price of the share without brokerage is:
[tex]C=50\times1000\times\frac{99.75}{100}=49875[/tex]The brokerage is given by:
[tex]B=49875\times\frac{6.5}{100}=3241.88[/tex]Hence the total cost of the sale is given by:
[tex]\begin{gathered} T=C+B \\ T=49875+3241.88 \\ T=53116.88 \end{gathered}[/tex]Hence the total cost of sale is $53116.88.
PointProduction chocolate barsProduction cans of colaA 0 100B 10 90C 20 70D 30 40E 40 0The above table shows production points on Sweet-Tooth Land's production possibilities frontier. Which of the following statements is TRUE?A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficientC.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficientD.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
First look and see if each of the values are true (attainable) before looking at efficiency
A.Producing 0 chocolate bars and 100 cans of cola is both attainable and efficient.
This is attainable
B.Producing 20 chocolate bars and 80 cans of cola is attainable but inefficient
This is not attainable
C.Producing 30 chocolate bars and 38 cans of cola is both attainable, with an inefficient
This is attainable
D.Producing 40 chocolate bars and 0 cans of cola is both attainable and inefficient
This is attainable
Now lets looks at efficiency
efficient when it is producing at the lowest point on the graph
Inefficient is below the graph
D should be efficient
A should be efficient
I am not sure why C is wrong
Raymond places four colored blocks in a bag. The colors are red, blue, yellow and green. Without looking, he reaches into the bag andpulls one block out.What is the probability that the block he pulls out will be yellow?A. 1/4. B.1/3. C.3/1. D.4/1
Given:
Total number of colored blocks in the bag = 4
Given that Raymond picks one block out without looking(randomly), let's find the probability it is a yellow block.
Probablity can be said to be the likelihood of the occurence of an event.
Given:
Number of yellow blocks = 1
To find the probability that the blocks he pulls out will be a yellow block, apply the formula below:
[tex]P(\text{yellow)}=\frac{\text{Number of yellow blocks}}{Total\text{ number of blocks}}[/tex]Thus, we have:
[tex]P(\text{yellow)}=\frac{1}{4}[/tex]Therefore, the probability thatvthe block he pulls out will be yellow is ¼
ANSWER:
[tex]A\text{. }\frac{1}{4}[/tex]How do i find the x intercept using the slope intercept form, graphing the y intercept, then using the slope to step to the x intercept. How do i know to go left or right for run?
How do i find the x intercept using the slope intercept form, graphing the y intercept, then using the slope to step to the x intercept.
slope intercept form is: y = mx + b where m = slope and b = y-intercept
Once you have your slope intercept equation, solve for m.
How do i know to go left or right for run?
slope = rise/run
if the number is negative, you will go left.
Please comment if you have further questions.
Lety = tan(3x + 3) . Find the differential dy when x = 5 and dx = 0.4
Applying the derivative of the trigonometric functions, the derivative of tan x is sec²x.
Hence, the derivative of tan (3x + 3 ) is sec² (3x + 3) times the derivative of 3x - 3 which is 3.
[tex]\begin{gathered} y=tan(3x+3) \\ dy=3sec^2(3x+3)dx \end{gathered}[/tex]To find the differential dy when x = 5 and dx = 0.4, simply replace the x and dx in the dy function with their given values.
[tex]dy=\lbrace3sec^2[(3(5)+3)]\rbrace(0.4)[/tex]Then, simplify.
[tex]dy=[3sec^2(18)](0.4)[/tex][tex]dy=3.3167(0.4)[/tex][tex]dy=1.32668\approx1.33[/tex]Hence, at x = 5 and dx = 0.4, the differential dy is approximately equal to 1.33.
For x = 5 and dx = 0.8, we do the same process above but this time, multiply the derivative by 0.8.
[tex]dy=[3sec^2(18)](0.8)[/tex][tex]dy=3.3167(0.8)[/tex][tex]dy=2.6534\approx2.65[/tex]Hence, at x = 5 and dx = 0.8, the differential dy is approximately equal to 2.65.
Construct an appropriate triangle to find the missing values
This can be solved using trigonometry.
What is trigonometry?
Trigonometry is a field of mathematics that examines correlations between triangle side lengths and angles (from the Ancient Greek words "trigonon" and "metron"). The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord computation. Trigonometry has been used historically in fields including geodesy, surveying, celestial mechanics, and navigation. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric similarities are frequently employed to rewrite trigonometrical statements.
Using trigonometric relations,
cos 30° = cos π/6 rad = √3/2
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