Answers
Answer:
5
Explanation:
Given the quotient:
[tex]61.32\div11.7[/tex]First, we estimate each of the numbers:
[tex]\begin{gathered} 61.32\approx60\text{ (to the nearest tens)} \\ 11.7\approx12\text{ (to the nearest whole number)} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 61.32\div11.7\approx60\div12 \\ =5 \end{gathered}[/tex]Related Questions
Determine the point (x, y) on the unit circle associated with the following real numbers. Write the exact answer as an ordered pair. Do not round.5xS-3
Answers
Given:
[tex]s=-\frac{5\pi}{3}[/tex]To find the point (x,y) on the unit circle:
The coordinate of the unit circle can be derived by,
[tex](\cos s,\sin s)[/tex]Substituting the value of s, we get
[tex]\begin{gathered} (\cos (-\frac{5\pi}{3}),\sin (-\frac{5\pi}{3}))=(\cos (2\pi-\frac{5\pi}{3}),\sin (2\pi-\frac{5\pi}{3})) \\ =(\cos (\frac{\pi}{3}),\sin (\frac{\pi}{3})) \\ =(\frac{1}{2},\frac{\sqrt[]{3}}{2}) \end{gathered}[/tex]Hence, the coordinate point on the unit circle is,
[tex](\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]Write an equation that can be used to find what ticket prices to set in order to raise $3800.If 200 adults attended and 250 children, find the cost of an adult ticket
Answers
Variables
x: cost of an adult ticket, in dollars
y: cost of a child ticket, in dollars
If 1 adult ticket is sold, then x dollars are raised. In consequence, if 200 adult tickets are sold, then 200x dollars are raised.
Similarly, if 250 child tickets are sold, then 250y dollars are raised.
Combining these amounts and raising $3800, we get:
200x + 250y = 3800
During your morning workout you run for 20 seconds for every 3 seconds you sprint. Write a proportion that shows the relationship between the number of seconds you run, the number of seconds you sprint, and the constant of proportionality
Answers
During your morning workout you run for 20 seconds for every 3 seconds you sprint. Write a proportion that shows the relationship between the number of seconds you run, the number of seconds you sprint, and the constant of proportionality
In the part 1 we calculate the constant of proportionality
k=20/3
Remember that
y -----> the number of seconds you run
x -----> the number of seconds you sprint
so
The linear equation that represent the relationship between x and y is
y=(20/3)x
the proprtion is
y/x=20/3k=20/3Part 3
Rewrite the proportion as an equation to represent the number of seconds you run in terms of the number of seconds you sprint
the proportion is
y/x=20/3
frewrite as equation
y=(20/3)x1. Which of the below is a binomial factor of thepolynomial shown?
Answers
The given polynomial is
[tex]\begin{gathered} 3x^2+11x+10^{} \\ \text{ By factoring completely, we obtain two paired factors 6 and 5,} \\ \text{ whose sum is 11 (the coefficient of x), and product 30 found from } \\ \text{ the product of the constant 10 and 3 (the coefficient of x}^2) \end{gathered}[/tex][tex]\begin{gathered} 3x^2+11x+10^{} \\ 3x^2+6x+5x+10 \\ 3x(x+2)+5(x+2) \\ (3x+5)(x+2) \end{gathered}[/tex]Therefore, a binomial factor of the polynomial is (x + 2) [Option A]
Carol is depositing $1500 into an account earning 3% compounded semiannually. How much money will be in the account after 25 years?
Answers
ANSWER
$3157.86
EXPLANATION
We have that Carol is depositing $1500 into an account earning 3% that is compounded semiannually.
The formula for amount for a compound interest is:
[tex]A\text{ = }P(1\text{ + }\frac{r}{n})^{n\cdot t}[/tex]where P = principal (amount deposited)
r = interest rate
t = number of years
n = number of times interest is compounded
Since the interest is compounded twice a year (semiannually), n = 2.
From the question:
P = $1500
r = 3% = 0.03
t = 25 years
So, the amount of money that will be there after 25 years is:
[tex]\begin{gathered} A\text{ = 1500(1 + }\frac{0.03}{2})^{2\cdot25} \\ A=1500(1+0.015)^{50} \\ \text{A = 1500(1.015)}^{50} \\ A\text{ = \$3157.86} \end{gathered}[/tex]SLV is a 45°-45°-90° triangle with leg SV. If SV = m, determine the length ofthe other leg and the hypotenuse.
Answers
Since angles S and L are congruent, the triangle SLV is isosceles with base SL, that means SV = LV.
Since SV = m, we have LV = m
Now, to calculate the hypotenuse, we can use Pythagorean theorem:
[tex]\begin{gathered} SL^2=SV^2+LV^2 \\ SL^2=m^2+m^2 \\ SL^2=2m^2 \\ SL=m\cdot\sqrt[]{2} \end{gathered}[/tex]Solve the following inequality. Give the solution set in both interval and graph forms -8 less than or equal to 2x+4 less than or equal to 14
Answers
The given inequality is -8 less than or equal to 2x+4 less than or equal to 14. In written form, we have
- 8 ≤ 2x + 4 ≤ 14
The first step is to subtract 4 from the left and right hand sides. We have
- 8 - 4 ≤ 2x + 4 - 4 ≤ 14 - 4
- 12 ≤ 2x ≤ 10
Dividing through by 2, we have
- 6 ≤ x ≤ 5
Which of the following expressions are equivalent to -19/8.(-50)?Choose all answers that apply.
Answers
To answer this question we notice the result of the original expression is positive; now, using the law of sign we notice that the negative sign in the fraction in option A will cancel out, leaving only the outer minus sign; after that if we make the product the result will be positve. This does not happens in option B, in this case the final result will be negative.
Therefore, the answer is A.
Which expressions are equivalent to the one below? Check all that apply. 212 32
Answers
Given:
[tex]\frac{21^x}{3^x}[/tex]Aim:
We need to find the equivalent expression for the given expression.
Explanation:
[tex]Use\text{ }\frac{a^n}{b^n}=(\frac{a}{b})^n.\text{ Here a=21, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=(\frac{21}{3})^x[/tex][tex]Use\text{ 21=7}\times3\text{ in the given expression.}[/tex][tex]\frac{21^x}{3^x}=\frac{(7\times3)^x}{3^x}[/tex][tex]Use\text{ }(a\times b)^x=a^x\times b^x.\text{ Here a=7, b=3 and n=x.}[/tex][tex]\frac{21^x}{3^x}=\frac{7^x\times3^x}{3^x}[/tex]Cancel out common terms.
[tex]\frac{21^x}{3^x}=7^x[/tex]Final answer:
[tex]B.\frac{7^x\times3^x}{3^x}[/tex][tex]C.\text{ }7^x[/tex][tex]D.\text{ }(\frac{21}{3})^x[/tex]
Ratio of boys to girls is 6 to 5. If there are 60 girls how many boys are there?
Answers
Given that
There are 60 girls and the ratio of boys to girls is 6:5.
Explanation -
Let the boys be b.
Then the ratio can be represented in fraction form as
[tex]\begin{gathered} \frac{b}{g}=\frac{6}{5} \\ \frac{b}{60}=\frac{6}{5} \\ b=\frac{6}{5}\times60=6\times12=72 \\ So\text{ there are 72 boys.} \end{gathered}[/tex]Hence, the final answer is 72.write 33_88 in simplest form
Answers
Answer
33 : 88 = 3 : 8
(33/88) = (3/8)
Explanation
33 : 88
THe best way is to do this is to divide both numbers by 11
(33/11) : (88/11)
= 3 : 8
Hope this Helps!!!
In the picture provided, describe the three dimensional figure that will be produced if the rectangle is rotated about the vertical axis.A. a cylinder with radius of 5 cm and height of 3 cm B.a cylinder with height of 5 cm and radius of 3 cm C. a cylinder with diameter of 5 cm and height of 3 cm D. a cylinder with height of 5 cm and diameter of 3 cm
Answers
To answer this question, we need to do a drawing like this:
If we see the figure from above, we will see that the figure will have a radius of 5 cm, and, therefore, a diameter of 10 cm. The height will be always 3 cm.
Therefore, if the rectangle is rotated about the vertical axis, we will have a cylinder of radius equal to 5 cm and a height of 3 cm.
Hence, the answer is option A: a cylinder with a radius of 5 cm and a height of 3 cm.
I solved part A of the problem I just need help solving part B
Answers
Given:
The function given is,
[tex]g(x)=0.009x-17.66[/tex]x represents the years.
Required:
The predicted increase in the temperature in the year 2011.
Explanation:
The predicted increase in the temperature in the year 2011 is given by,
[tex]\begin{gathered} g(2011)=0.009\times(2011)-17.66 \\ \Rightarrow g(2011)=0.439 \\ \Rightarrow g(2011)=0.4\degree \end{gathered}[/tex]Final Answer:
[tex]0.4\degree C[/tex]What is the location of the point (5, 0) translates 4 units to the down and reflected across the y-axis?
Answers
STEP-BY-STEP EXPLANATION:
Given information
The given ordered point = (5, 0)
Step 1: We need to translate the point 4 units down
To translate down means we will be subtracting a value from the y--axis
Hence, we have
[tex]\begin{gathered} (x,\text{ y) }\rightarrow\text{ (x, y-b)} \\ \text{where b = 4} \\ (5,\text{ 0) }\rightarrow\text{ (5, 0 - 4)} \\ (5,\text{ 0) }\rightarrow\text{ (5, -4)} \end{gathered}[/tex]When translated 4 units down, we got (5, -4)
Step 2: Reflect over the y-axis
The general rule for reflecting over the y-axis is (-x, y)
This means the value of x will be negated and the value of y will remain the same
[tex]\begin{gathered} \text{Over the y-ax}is \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (5,\text{ -4) }\rightarrow\text{ (-5, -4)} \end{gathered}[/tex]Step 3: the graph the point
When multiplying or dividingpolynomials using the Tabular Method, write the number of terms for the polynomial ax^2+bx+c
Answers
Explanation
Answer
The number of terms for the polynomial is 3
The mean score on a Statistics exam is 88 points, with a standard deviation of 6 points. Apply Chebychev's Theorem to the data using k=2. Interpret the results.
Answers
Step 1
Given;
Step 2
State Chebychev's theorem
Thus;
[tex]\begin{gathered} k=2 \\ 1-\frac{1}{2^2}=1-\frac{1}{4}=\frac{3}{4} \end{gathered}[/tex]The empirical formula that applies to this is about 2 standard deviations of the mean
[tex]\begin{gathered} (\mu+2\sigma)\text{ and \lparen}\mu-2\sigma) \\ (88+2(6))\text{ and \lparen88-2\lparen6\rparen\rparen} \\ 100\text{ and 76} \end{gathered}[/tex]Answer;
[tex]At\text{ least 75\% of the exam scores falls between 76 and 100}[/tex]A book sold 37,900 copies in its first month of release. Suppose this represents 9.1% of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
Answers
We know that 9.1% of the total copies sold are 37,900.
If we call N to the total amount of copies sold and see that 9,1% correspond to a proportion of 9.1/100=0.091, we can calculate N as:
[tex]\begin{gathered} 0.091\cdot N=37,900 \\ N=\frac{37,900}{0.091} \\ N\approx416,484 \end{gathered}[/tex]Answer: the total number of copies sold is approximately 416,484.
Artemis starts his hike at an elevation of 350 feet. He descends 60 feet, ascends 135 feet, ascends 250 feet, and finally descends 128 feet. Which equation describes his final elevation in feet? 350 + 60 + 135 + 250 + 128 = 923 B 350 + (-60) + 135 + 250 + 128 803 C 350 + (-60) + 135 + 250 + (-128) = 547 D 350 + (-60) + 135 + (-250) + 128 = 303
Answers
Total 350feet
Note descend you subtract and ascend you add
350-60+135+250-128=547
The correct option is C
Find the value of y at which the maximum occurs
Answers
Given
Z = 2x + y
Find
Find the value of y at which the maximum occurs
Explanation
objective function is maximum at point (12 , 0)
so , here value of x = 12
and value of y = 0
therefore ,
value of y at which the maximum occurs = 0
Final Answer
hence , x = 12 and y = 0
write 2.25% as fraction to the simplest form
Answers
2.25% can also be written as 0.0225 if we divide 2.25% by 100% and we eliminate the percentages:
To make the decimal 0.0225 a fraction, we have to multiply by a number in which the decimal will be an integer:
[tex]\frac{0.0225}{1}\times\frac{10000}{10000}=\frac{225}{10000}[/tex]Simplifying the fraction obtained:
[tex]\frac{225}{10000}=\frac{9}{400}[/tex]Answer:
[tex]\frac{9}{400}[/tex]16For an arithmetic series a₁ = -10 and S6 = -285, find the common difference.A-35B-25C -15D -5
Answers
Given:
An arithmetic series a₁ = -10 and S6 = -285
We will find the common difference (d) using the formula of the sum.
[tex]S=\frac{n}{2}(2a+(n-1)d)[/tex]Substitute S= -285, a = -10, n = 6
[tex]\frac{6}{2}(2(-10)+(6-1)d)=-285[/tex]Solve the equation to find (d):
[tex]\begin{gathered} 3(-20+5d)=-285 \\ -20+5d=-\frac{285}{3} \\ \\ -20+5d=-95 \\ 5d=-95+20 \\ 5d=-75 \\ \\ d=-\frac{75}{5}=-15 \end{gathered}[/tex]So, the answer will be option C) -15
Point O is the center of this circle. What is m
Answers
If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees
The point o is the center of the circle
∠COB = 96 degrees
Here we have to apply the circle theorem
The circle theorem is defined as the measure of angles joined to any point on the circumference of the circle from the same arc is equal to the one by two of the angle subtended at the center by the same arc.
Then the equation will be
∠COB = 2 × ∠CAB
Substitute the values in the equation
2 × ∠CAB = 96
∠CAB = 96 / 2
Divide the terms
∠CAB = 48 degrees
Hence, If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees
Learn more about circle theorem here
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what is 2/13×2/4?what is 2 * 3 what is 5 * 3 hey what is the answer
Answers
y=20-4x. the volume of the box is V cm ^3 find in terms of x
Answers
b. The volume of a box is computed as follows:
[tex]V=\text{length}\cdot\text{width}\cdot\text{height}[/tex]Substituting with length = 3x, width = x, and heigth = y = 20 - 4x, we get:
[tex]\begin{gathered} V=3x\cdot x\cdot(20-4x) \\ V=3x^2(20-4x) \\ V=3x^2\cdot20-3x^2\cdot4x \\ V=60x^2-12x^3 \end{gathered}[/tex]c.
[tex]\frac{d}{dx}(x^n)=n\cdot x^{n-1}[/tex]Applying this rule to V, we get:
[tex]\begin{gathered} \frac{dV}{dx}=60\cdot2\cdot x-12\cdot3\cdot x^2 \\ \frac{dV}{dx}=120x-36x^2 \end{gathered}[/tex]What is the surface area of the cylinder with height of 6cm and radius of 7cm?Round your answer nearest thousanddth
Answers
The radius of cylinder is r=7 cm.
The heighht of cylinder is h= 6 cm
Determine the surface area of the cylinder.
[tex]\begin{gathered} SA=2\pi rh+2\pi(r)^2 \\ =2\pi\cdot7\cdot6+2\pi\cdot(7)^2 \\ =572 \end{gathered}[/tex]So answer is 572 centimeter square.
For Items 9-11, determine the length of each segmentwith the given endpoints.9. C(1, 4) and D(11, 28)10. Y(-2, 6) and Z(5, -8)11. P(-7,-7) and Q(9,5)
Answers
Use the following formula:
d = √((x2-x1)² + (y2-y1)²)
9.
C(1,4) = (x1,y1)
D(11,28) = (x2,y2)
d = √((11-1)² + (28-4)²) = √((10)²+(24)²) = 29.73213749
10.
Y(-2,6) = (x1,y1)
Z(5,-8) = (x2,y2)
d = √((5-(-2))² + (-8-6)²) = √((7)² + (-14)²) = 15.65247584
11.
P(-7,7) = (x1,y1)
Q(9,5) = (x2,y2)
d = √((9-(-7))² + (5-(-7))²) = √((16)²+(12)²) = 20
10. A glass jar contains 8 red, 6 green, 12 blue, and 10 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a(a) red marble? (b) green marble? (c) blue marble?
Answers
Let:
• A ,be the event of getting a red marble
,• B ,be the event of getting a green marble
,• C ,be the event of getting a blue marble
We'll have that:
[tex]\begin{gathered} P(A)=\frac{8}{36} \\ \\ P(B)=\frac{6}{36} \\ \\ P(C)=\frac{12}{36} \end{gathered}[/tex]What is the range of the function?Type the answer using interval notation example : (#,#]
Answers
To analyze the range we need to look at the Y values. In this case the lowest Y value is 0 and the highest Y value it can go all the way up to positive infinity. So the range would be [0, +∞)
last Friday Adam had $22.33 over the weekend, she received some money for cleaning the attic period. He now had 32 dollars period, how much money did he receive.
Answers
Word Problem Leading to Simple Equation.
Last Friday Adam had $22.33 : 22.33
He received some money for cleaning: Let the amount of money he received be x, so that she now has:
[tex]22.33+x[/tex]He is left with $32, meaning his total money is now $32 :
Mathematically, we write:
[tex]\begin{gathered} 22.33+x=32 \\ \text{Collecting like terms, we get,} \\ x=32-22.33 \\ x=\text{ \$9.67} \end{gathered}[/tex]Hence, the correct answer is $9.67
Write a linear cost function for the following situation. Identify all variables used.A ski resort charges a snowboard rental fee of $20 plus $5.50 per hour.GLEEDIdentify all variables used. Choose the correct answer below.A. C(t) represents the number of hours the snowboard was used after renting a snowboard for t dollars.B. C(t) represents the number of snowboards that can be rented for t dollars.C. C(t) represents the cost for renting t snowboards.D. C(t) represents the cost of renting a snowboard for t hours.A linear cost function for the situation is C(t) =___(Use integers or decimals for any numbers in the expression.)
Answers
GIVEN:
We are told that a ski resort charges a snowboard rental fee of $20 plus $5.50 per hour.
Required;
Select the correct option to represent the meaning of C(t).
Also, write a linear function for the situation;
Step-by-step solution;
For the rental per hour, a fee of $5.50 is charged, which means for t number of hours, the rental would be 5.50 times t or, 5.50t. Note also that a fixed rental fee of $20 is already included regardless of how many hours rental is paid. This now means the rental would be $20 plus $5.50t.
Note that the variable t represents how many hours the snowboard was rented for. Therefore, we have;
ANSWER:
Option D:
C(t) represents the cost of renting a snowboard for t hours
A linear cost function for the situation is;
[tex]C(t)=20+5.50t[/tex]