Mathematics College
Answers
Answer 1
The given diameater of the soccer ball is 8(5/3).
Convert the mixed number to real number,
Related Questions
is the spike in share price an example of exponential growth?
Answers
Explanation:
For an exponential growth, the spike in share price must be proportional to what was already on ground.
We conclude that it is not an example of exponential growth.
The slope of the line that passes through the points (2,4) and (-1,9) is
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Given the points (2,4) and (-1,9)
[tex]\begin{gathered} X_1=2;Y_1=4 \\ X_2=-1;Y_2=9 \end{gathered}[/tex][tex]\begin{gathered} \text{Slope, M of a line is given by the equation;} \\ M=\frac{Y_2-Y_1}{X_2-X_1} \\ M=\frac{9-4}{-1-2} \\ M=\frac{5}{-3} \\ M=\frac{-3}{5} \end{gathered}[/tex][tex]\text{Hence the slope of the l}ine\text{ }is\text{ }\frac{-3}{5}[/tex]
You have to decide which of two prizes you will accept! • Prize A: $5,000 for the first month with a $100 increase every month thereafter. • Prize B: $2,000 for the first month with a 10% increase every month thereafter.A) Create an equation for each situation (Prize A and Prize B). B) Use each equation to complete the table to the right.C) When will prize B earn more than prize AD) How much more will prize B earn than prize A in the 12th month?
Answers
Answer:
(c)12th Month
(d)$76.86
Explanation:
Part A
Prize A: $5,000 for the first month with a $100 increase every month thereafter.
[tex]y_1=5,000+100x[/tex]
Prize B: $2,000 for the first month with a 10% increase every month thereafter.
[tex]\begin{gathered} y_2=2000(1+\frac{10}{100})^x \\ y_2=2000(1.1)^x \end{gathered}[/tex]
Part B
The table is completed and attached below:
Part C
As seen from the table, Prize B will earn more than prize A in the 12th Month.
Part D
[tex]\begin{gathered} \text{Difference in the 12th Month=6276.86-6200} \\ =\$76.86 \end{gathered}[/tex]
Prize B will earn $76.86 more than prize A in the 12th month.
what is the equation of the line that passes through blank and is parallel to the line blank
Answers
Given the equation:
y = 3x + 2
Let's find the equation that passes through the point (3, -1) and is parallel to the given line.
Apply the slope-intercept form of a linear equation:
y = mx + b
Where m is the slope and b is the y-intercept.
Now compare both equations:
y = mx + b
y = 3x + 2
This means the slope of the line m = 3.
y-intercept (b) = 2
The slope of parallel lines are equal.
Hence, the slope of the parallel line is also 3.
Now, let's find the y-intercept of the parallel line.
Given the point:
(x, y) ==> (3, -1)
Substitute 3 for x, -1 for y, then 3 for m in the slope-intercept equation to solve for b.
We have:
y = mx + b
-1 = 3(3) + b
-1 = 9 + b
Subtract 9 from both sides:
-1 - 9 = 9 - 9 + b
-10 = b
b = -10
The y-intercept of the parallel line is -10.
Therefore, the equation of the parallel line is:
y = 3x - 10
Given v = 4i - j and w = 2i + 5j, find the angle between v and w
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Angle between v and w is
Angle A = Angle v - Angle w
then
Angle v= Arctan (-1/4) = -14 °
Angle w= Arctan (5/2) = 68.2 °
Therefore, angle between v and w is
. = -82.2 °
Then answer is
Angle A = -82.2°
Use simple interest to find the ending balance. Round to the nearest cent when necessary. $215 at 8% for 8 years,
Answers
The formua for determining simple interest interest is expressed as
I = PRT/100
where
I = interest
P = principal or initial amount
R = interest rate
T = number of years
From the information given,
P = 215
T = 8
R = 8
I = (215 x 8 x 8)/100 = 137.6
The ending balance after 8 years = principal + intereest
Ending balance = 215 + 137.6 = $352.6
3. Jared is inviting his friends to a party. He has 48 fruit snacks and 63 co*kes, and he wants to givethe same number of each item to each friend. What is the greatest number of friends that Jaredcan invite over? How many fruit snacks and co*kes will each friend get?
Answers
To solve the exercise, we are going to find the greatest common factor or GCF of 48 and 63:
• Factors of 48: 1, 2, ,3,, 4, 6, 8, 12, 16, 24, and 48.
• Factors of 63: 1, ,3,, 7, 9, 21, and 63.
Notice that the greatest common factor of 48 and 63 is 3.
Therefore, the greatest number of friends that Jared can invite over is 3.
For the second question, we divide the number of fruit snacks by the number of friends that Jared can invite, and we divide the number of co*kes by the number of friends that Jared can invite:
[tex]\begin{gathered} \frac{48}{3}=16\Rightarrow\text{ Fruit snacks} \\ \frac{63}{3}=21\Rightarrow\text{ co*kes} \end{gathered}[/tex]
Therefore, each friend will receive 16 fruit snacks and 21 co*kes.
8. *Write the equation of the graph shown below. 6 4
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The reflected graph of the function y=|x| is shown below.
The graph of -y=|x| is,
In the question, the vertex of graph is translated 2 units to left implies,
[tex]-y=|x+2|[/tex]
The vertex is shifhted four units above, implies,
[tex]-y=|x+2|-4[/tex]
Therefore, the equation is
y=-|x+2|+4
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.Match each logarithmic equation to its corresponding x-value.
Answers
Answer:
[tex]\begin{gathered} a)\text{ log}_{10}x\text{ =3 }\rightarrow\text{ 1000} \\ b)\text{ log}_2x\text{ = 5}\rightarrow\text{ 32} \\ c)\text{ log}_4x\text{ = 2 }\rightarrow\text{ 16} \\ d)\text{ log}_5x\text{ = 4}\rightarrow\text{ 625} \end{gathered}[/tex]
Explanation:
Here, we want to select the appropriate logarithmic relationship
We have the general rule as:
[tex]\begin{gathered} Log\placeholder{⬚}_aB\text{ = c} \\ B\text{ = a}^c \end{gathered}[/tex]
This is the rule we are going to use. Since there are 4 tiles, we shall be selecting the 4 logarithmic expressions and use their number equivalent on the right side
a)
[tex]\begin{gathered} log\placeholder{⬚}_{10}\text{ x = 3} \\ x\text{ = 10}^3 \\ x\text{ = 1000} \end{gathered}[/tex]
b)
[tex]\begin{gathered} log\placeholder{⬚}_2x\text{ = 5} \\ x\text{ = 2}^5 \\ x\text{ = 32} \end{gathered}[/tex]
c)
[tex]\begin{gathered} log\placeholder{⬚}_4x\text{ = 2} \\ x\text{ = 4}^2 \\ x\text{ = 16} \end{gathered}[/tex]
d)
[tex]\begin{gathered} log\placeholder{⬚}_5x\text{ = 4} \\ x\text{ = 5}^4 \\ x\text{ = 625} \end{gathered}[/tex]
Solve for x.-8x - 3 4x + 3When angles form a linear pair, their sum is 180°.8x - 3+ 4x + 3 = 18012x + [?]== 180Hint: Calculate the sum of 3 and -3 and enter its value.
Answers
Notice that:
[tex]-3+3=0.[/tex]
Therefore:
[tex]8x-3+4x+3=12x+0.[/tex]
Answer: ?=0.
The sum of 5/6 and twice a number is equal to 2/3 subtracted from three times the number. Find the number
Answers
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Interpret the statement
Let the number be y
From first statement,
[tex]\begin{gathered} twice\text{ the number}=2y \\ 2y+\frac{5}{6}=3y-\frac{2}{3} \end{gathered}[/tex]
STEP 2: Evaluate the equation to get y
[tex]\begin{gathered} \mathrm{Subtract\:}\frac{5}{6}\mathrm{\:from\:both\:sides} \\ 2y+\frac{5}{6}-\frac{5}{6}=3y-\frac{2}{3}-\frac{5}{6} \\ 2y=3y-\frac{3}{2} \\ \mathrm{Subtract\:}3y\mathrm{\:from\:both\:sides} \\ 2y-3y=3y-\frac{3}{2}-3y \\ -y=-\frac{3}{2} \\ \mathrm{Divide\:both\:sides\:by\:}-1 \\ \frac{-y}{-1}=\frac{-\frac{3}{2}}{-1} \\ y=\frac{3}{2} \end{gathered}[/tex]
Hence, the number is 3/2
[-14, -8] U (-8, 10)
Answers
The symbol U means that we are going to do the Union of two sets, which means that we will take the elements of set A, and the elements of set B, and create a new set C that contains all the elements of A and B.
Therefore, if A = [-14, -8] and B = (-8, 10), the union of that two sets, represented by [-14, -8] U (-8, 10) will be
[tex]C=\lbrack-14,10)[/tex]
Final answer:
[tex]C=\lbrack-14.10)[/tex]
a + 2a - 3 = 30and 0.10c + 0.25(c + 3) = 10.90
Answers
[tex]a+2a-3=30[/tex]
solve the first squation by simplifying all common factors
[tex]3a-3=30[/tex]
add 3 on both sides
[tex]\begin{gathered} 3a-3+3=30+3 \\ 3a=33 \end{gathered}[/tex]
divide by 3 on both sides
[tex]\begin{gathered} a=\frac{33}{3} \\ a=11 \end{gathered}[/tex]
for the second equation
[tex]0.10c+0.25(c+3)=10.90[/tex]
simplify left side of the equation
[tex]0.10c+0.25c+0.75=10.90[/tex][tex]0.35c+0.75=10.90[/tex]
substract 0.75 on both sides
[tex]\begin{gathered} 0.35c+0.75-0.75=10.90-0.75 \\ 0.35c=10.15 \end{gathered}[/tex]
divide by 0.35 on both sides
[tex]\begin{gathered} c=\frac{10.15}{0.35} \\ c=29 \end{gathered}[/tex]
Rewrite the given rational expression in the form q(x) + r(x)/b(x) where q(x) = quotient, r(x) = remainder, and b(x) = divisor.(x3 – x – 23)/(x + 1)- x2 –x(x2 – x)– 23/(x + 1)x2+ x(-x2 + x)– 23/(x + 1)
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Given
[tex]\frac{x^3+2x^2+3x+2}{x+1}[/tex]
To rewrite the expression using synthetic division.
Explanation:
It is given that,
[tex]\frac{x^3+2x^2+3x+2}{x+1}[/tex]
That implies,
Set x + 1 = 0.
Then, x = -1.
Therefore, by using synthetic division,
Hence, the expression is rewritten as,
[tex]x^2+x+2[/tex]
Find the length of the unknown side of the right triangle with sides a, b, and c, where c is the hypotenuse.
Answers
Answer: The lengths of the triangles with the sides a b and c can be visualized as follows:
Using the Pythagorean theorem, we can construct the following equation related to the triangle shown:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \\ \\ a=\sqrt{9} \\ b=? \\ c=9 \\ \\ \\ (\sqrt{9})^2+b^2=9^2 \\ \\ \\ b^2=9^2-(\sqrt{9})^2 \\ \\ b=\sqrt{81-9}=\sqrt{72}\approx8.4853 \end{gathered}[/tex]
Eve’s gecko eats 2/7 jar of baby food a day . She has 10 jars of baby food. How many days can she feed her gecko with this food ?
Answers
Answer: 35 days
Explanation:
We have that 2/7 of a jar are use per day to feed the gecko. If she has 10 jars, what we need to do is divide 10 days by 2/7 per day, and we will find the number of days that she can feed her gecko.
-Divide 10 by 2/7:
10 ÷ 2/7
this is equal to the following:
[tex]\frac{10\cdot7}{2}[/tex]
we multiply 10 by the denominator 7 and divide by 2.
solving the operations:
[tex]\frac{10\cdot7}{2}=\frac{70}{2}=35[/tex]
How many days can she feed her gecko with this food ? 35
Part BFlip a penny 50 times and tally the results in the table provided, using an X for each tally mark. Write the total number of heads and the totalnumber of tails below the table. If you don't have a penny available, use the data provided.Heads TailsХХХХХХХХХХXXXXXXXXXXXXXXXХХХХХХХХХХXXXXXXXXXX
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We are only tasked to count the total number of heads and tails provided by the table. Each X represents a flip that resulted in heads/tails. Based on the given table, the number of heads and tails are
Head - 28
Tails - 22
Select all the values that are equivalent to the given expression. Express your answer in scientific notation.(9.6times10^3)times(6.7times10^2)A. 6.432times10^5B. 6.432times10^6C. 64.32times10^5D. 64.32times10^6E. (9.6times6.7)times(10^3times10^2)
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The given expression is
[tex](9.6\times10^3)\times(6.7\times10^2)[/tex]
First, we group factors and powers.
[tex](9.6\times6.7)(10^3\times10^2)[/tex]
Then, we multiply.
[tex]\begin{gathered} 64.32\times10^{3+2} \\ 64.32\times10^5 \end{gathered}[/tex]Therefore, the right answer is C.
A student measures the amount of water, x, that his classmates drink during one day and compares it to the amount of sleep, y, that they get. When he computes the correlation coefficient, he gets 1.18. What does that say about the relationship between the amount of water and amount of sleep?
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The correlation coefficient gives information about the behavior of two variables and it should always be between -1 and 1.
Since the value of the correlation coefficient is 1.18, then the student made an error computing the correlation coefficient, because the number has to be between -1 and 1.
When the coefficient is near the value of 1, it means that there is a strong positive relationship between the variables (y increases as x increases).
When the coefficient is near the value of -1, it means that there is a strong negative relationship between the variables (y decreases as x increases).
When the value is not near 1 or -1, and it's rather near to 0, then there is a weak relationship (it will be a positive or negative relationship depending on the sign).
Either case, the coefficient cannot be greater than 1 or lower than -1.
points E,D and H are the midpoints of the side of TUV. UV=62,TV=80,and HD=62,Find TU.
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The given triangle, is TUV
As E, D, H are the midpoints, we have,
HE=1/2 UV
Similarly,
[tex]\begin{gathered} HD=\frac{1}{2}TU \\ 62=\frac{1}{2}TU \\ TU=2\times62=124 \end{gathered}[/tex]
convert the product into a polynomial: (4x^2y+3xy-x^2)(-x^3y^2)
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The product is:
[tex](-x^3y^2)(4x^2y+3xy-x^2)[/tex]
What we have to do is to distribute the -x^3 y^2 term over the other three terms:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]
In the first term I did:
[tex]-x^3y^2\times4x^2y=-4x^5y^3[/tex]
The second term was:
[tex]-x^3y^2\times3xy=-3x^4y^3[/tex]
And finally, the third term:
[tex]-x^3y^2\times-x^2=x^5y^2[/tex]
Then the answer is:
[tex]-4x^5y^3-3x^4y^3+x^5y^2[/tex]
Travis converted some repeating decimals into fractions as follows based upon what he has seen so far which of the following equations must be correct I'll take a pic to show you
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Answer:
[tex]0.\bar{9}=1[/tex]
Explanation:
The fractions are formed with a 9 as a denominator and the numerator is the number that repeats. So, following the same rule, we can say that 0.999... is equivalent to:
[tex]0.\bar{9}=\frac{9}{9}[/tex]
However, 9/9 is equal to 1, so:
[tex]0.999\ldots=0.\bar{9}=1[/tex]
Therefore, the answer is:
[tex]0.\bar{9}=1[/tex]
what is x? how would i find the value of x?
Answers
Given
Find
Value of x
Explanation
Here , we use trigonometric ratio
[tex]\begin{gathered} \tan C=\frac{P}{B} \\ \\ \tan65\degree=\frac{AB}{BC} \\ \\ \tan65\degree=\frac{x}{7} \\ \\ x=7\tan65\degree \\ \\ x=15.0115484436\approx15 \end{gathered}[/tex]
Final Answer
Hence , the value of x is 15
what was the bill subtotal if a customer left a $22 tip that was 20%?
Answers
We know that the tip was $22, which represents 20% of the total, Ti dubs the bill subtotal, we have to solve the following proportion
[tex]\frac{22}{0.20}=\frac{x}{1}[/tex]
Let's solve for x
[tex]x=110[/tex]Hence, the bill subtotal was $110.
Factor f(x) = 4x² + 28x + 48
Answers
ANSWER
4(x + 3)(x + 4)
EXPLANATION
We want to factorise:
4x² + 28x + 48
We simply want to write the expression as a product of its factors.
First, because each of the coefficients in the expression and the constant are divisible by 4, we will factor out 4:
[tex]4(x^2\text{ + 7x + 12)}[/tex]
Now, we have to look for two numbers such that adding them will yield 7 and their product will yield 12.
The two numbers we need are:
3 and 4
So, we have that the expression becomes:
[tex]\begin{gathered} 4(x^2\text{ + 3x + 4x + 12)} \\ \Rightarrow\text{ 4\lbrack{}x(x + 3) + 4(x + 3)\rbrack} \\ \Rightarrow\text{ 4(x + 3)(x + 4)} \end{gathered}[/tex]
We have factorised it.
The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
Answers
Given:
The table of the frequency distribution of the weights (in grams) of pre-1964 quarters is given.
Required:
Find the correct histogram from the given histogram.
Explanation:
We can observe from the given histogram that the frequency from 6.150-6.199 to 6.200-6.249 is decreasing. In histogram B it is increasing So option B is not the correct answer.
In histograms A and C we will observe that the frequency is 6.000-6.049
3 and 6.350-6.399 are 1.
But by observation in histogram A it is not correct.
It is correct in histogram C.
Final Answer:
Option C is the correct answer.
Write an equation of variation to represent the situation and solve for the missing information The number of revolutions made by a tire traveling over a fixed distance varies inversely tothe radius of the tire. A 12-inch radius tire makes 100 revolutions to travel a certaindistance. How many revolutions would a 16-inch radius tire require to travel the samedistance?
Answers
74.97 revolutions
Explanation
Step 1
The number of revolutions made by a tire traveling over a fixed distance varies inversely to
the radius of the tire
Let
The number of revolutions=n
the radius of the tire:r
then
[tex]n=\frac{\lambda}{r}[/tex]
where
[tex]\lambda\text{ is a constant}[/tex]
A 12-inch radius tire makes 100 revolutions to travel a certain,Hence
[tex]\begin{gathered} n=\frac{\lambda}{r} \\ 100=\frac{\lambda}{12} \\ \text{Multiply both sides by 12} \\ 100\cdot12=\frac{\lambda}{12}\cdot12 \\ 1200=\lambda \end{gathered}[/tex]
so, the constant is 1200, the equation is
[tex]\begin{gathered} n=\frac{\lambda}{r} \\ n=\frac{1200}{r}\text{ equation} \end{gathered}[/tex]
then, we need to find the distance
then
[tex]\begin{gathered} a\text{ revolution=2}\cdot\pi\cdot radius \\ a\text{ revolution=2}\cdot\pi\cdot12\text{ inche( for the first tire)} \\ a\text{ revolution=75.38 inches} \\ \text{then 100 revolutions = 100}\cdot75.38\text{ inches} \\ 100\text{ revolutionss=7539 inches} \end{gathered}[/tex]
then,the distance is 7539 inches
Step 2
Let
n= unknown
radius=r=16 inch
distance=7539 inches
[tex]\begin{gathered} 2\cdot\pi\cdot r=2\cdot\pi\cdot16 \\ 32\cdot\pi=100.53\text{ inches} \end{gathered}[/tex]
it means
[tex]1\text{ revolution}\Rightarrow100.53\text{ inches}[/tex]
then
[tex]\nu\text{mber of revolutions}\cdot100.553=same\text{ distance}[/tex]
replacing
[tex]\begin{gathered} N\cdot100.553=7539\text{ inches} \\ \text{divide both sides by 100.553} \\ \frac{N\cdot100.553}{100.553}=\frac{7539}{100.553} \\ N=74.97\text{ revolutions} \end{gathered}[/tex]
6. A war veteran and a senior citizen are each buying the same model of vacuum cleaner for $115. They are each going to use their coupons, which say respectively "Veterans receive 20% off all store items!" and “Senior discount $50!". Who gets the better deal?
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EXPLANATION
Vacuum cleaner = $15
Coupon discount [For Veterans]= 20%
Seniors discount = $50
To compare both we can do:
Veterans---> $115 * 0.80 = $92
Seniors-----> $115 -50 = $65
Answer: Seniors get the better deal.
[tex](6 \times (4 - 2) + (21 \times \frac{2}{3} + 1)) \div \frac{3}{2} [/tex]
Answers
Find calculation of fractions
Zeros algebra two help
Answers
we have the function
[tex]y=\frac{x^2+7x+10}{x+3}[/tex]
Remember that
The zeros of the function, are the values of x when the value of y=0
so
For y=0
[tex]x^2+7x+10=0[/tex]
Solve the quadratic equation
we have that
x^2+7x+10=(x+5)(x+2)
therefore
the zeros of the function are
(-5,0) and (-2,0)