5. Solve the division expression from the problem above (4 + 3). 4 3 A. 12 B. 1 c. 13 D. 14 3
Answers
A division as follow:
[tex]\frac{4}{3}[/tex]Can be solve as:
4/3 is equal to sum 1/3 four times:
[tex]\frac{4}{3}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}[/tex]As 3/3 is equal to 1 unit:
[tex]=1+\frac{1}{3}[/tex]Writen as a mixed number:
[tex]1\frac{1}{3}[/tex]Related Questions
2. Identify each measurement as the diameter, radius, or circumference of the circular
object. Then, estimate the other two measurements for the circle.
a. The length of the minute hand on a clock is 5 in.
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ANSWER:
Diameter: 10 in
Radius: 5 in
Circumference of the circular: 31.4 in
STEP-BY-STEP EXPLANATION:
The minute hand represents the radius of the clock, therefore the radius is 5 inches. The diameter is twice the radius, so they would equal 10 inches.
And we calculate the circumference like this:
[tex]\begin{gathered} c=2\cdot\pi\cdot r \\ c=2\cdot3.14\cdot5 \\ c=31.4\text{ in} \end{gathered}[/tex]Triangle A has points/coordinates of C(-2, 4), D(-3, 2), E(-1, 1). List the coordinates of the new image after Triangle A is reflected across the Y-axis.
Answers
The coordinate points of the triangle are:
[tex]\begin{gathered} C\mleft(-2,4\mright) \\ D\mleft(-3,2\mright) \\ E\mleft(-1,1\mright) \end{gathered}[/tex]The graph of this original points is as follows:
Now, to make the reflection across the Y-axis, we follow this rule of transformation:
[tex](x,y)\longrightarrow(-x,y)[/tex]so the points become the following:
[tex]\begin{gathered} C^{\prime}(2,4) \\ D^{\prime}(3,2) \\ E^{\prime}(1,1) \end{gathered}[/tex]Which, if we graph them, we get :
Answer:
[tex]\begin{gathered} C^{\prime}(2,4) \\ D^{\prime}(3,2) \\ E^{\prime}(1,1) \end{gathered}[/tex]Hot Air Balloon Tours, Inc. must pay the bank $23,515.27 in interest 200 days after making a loan of $328,120 to purchase hot air balloons. What is the interest rate? Round to the nearest tenth of a percent
Answers
To solve this problem we will use the formula for compound interest:
[tex]P_N=P_0\cdot(1+\frac{r}{k})^N\text{.}[/tex]Where:
• P_N is the balance in the account after N years,
,• P_0 is the starting balance of the account (also called an initial deposit, or principal),
,• r is the annual interest rate in decimal form,
,• N in years,
,• k is the number of compounding periods in one year.
In this problem, we have:
• P_0 = $328,120,,
,• interest P_N - P_0 = $23,515.27 → ,P_N = $351,635.27,,
,• N = ,200 days = ,200/365,
,• k = 1.
From the formula above, we have:
[tex]\begin{gathered} (\frac{P_N}{P_0})^{\frac{1}{N}}=1+r \\ r=(\frac{P_N}{P_0})^{\frac{1}{N}}-1. \end{gathered}[/tex]Replacing the data of the problem, we get:
[tex]r=(\frac{351,635.27}{328,120})^{\frac{365}{200}}-1\cong0.1346\cong13.5％.[/tex]Answer
The annual interest is 13.5%.
The two numbers that I said were closest together were 0.17 and 0.128
Answers
First, write the numbers 0.17 and 0.128 as a fraction. To do so, remember that if the denominator is not visible, we can consider it as equal to 1:
[tex]\begin{gathered} 0.17=\frac{0.17}{1} \\ 0.128=\frac{0.128}{1} \end{gathered}[/tex]Multiply both numerator and denominator by 1000:
[tex]\begin{gathered} 0.17=\frac{0.17\cdot1000}{1\cdot1000} \\ =\frac{170}{1000} \end{gathered}[/tex][tex]\begin{gathered} 0.128=\frac{0.128\cdot1000}{1\cdot1000} \\ =\frac{128}{1000} \end{gathered}[/tex]Since both 128/1000 and 170/1000 have the same denominator, we can find another fraction between both of them just by finding a number between the numerators. This is, a number between 128 and 170.
Since 128<150<170, then a fraction between 128/1000 and 170/1000 is:
[tex]\frac{150}{1000}[/tex]Therefore:
[tex]0.128<\frac{150}{1000}<0.17[/tex]5) Point G is rotated counter-clockwise about H and by an angle of 45°. If it's image is G Prime and segments GH, G prime H, G prime G prime are drawn which of the following is true ? A)GH is congruent to G prime HB) Gh is perpendicular to G prime HC) Gh is parallel to G prime H D) H is the midpoint of segment G prime G
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We are given that a point is rotated counterclockwise about an angle of 45 degrees. A diagram of this is the following:
Now, since the rotation of point G to point G' won't affect the distance of segment GH, this means that
[tex]GH=G^{\prime}H[/tex]Rotation is a type of transformation called isometries, that is, transformations that do not change the distance.
Algebra 1Simplify each expression by using the Distributive Property and combine like terms to simplify the expression.-(3n-5)-7n
Answers
-(3n-5)-7n
Apply the distributive property to distribute the negative sign:
-(3n)-(-5)-7n
-3n+5-7n
Combine like terms ( the ones with "n")
-3n-7n+5
-10n+5
the triangle will be rotated 270 degrees counter clockwise about the origin click in each vertex of the rotated triangle starting and ending of the same vertex
Answers
Coordinates
(0,0)
(0,6)
(-6,5)
1. The graphs show the distance, d, traveled by two cars, A and B, over time, T Distance is measured in miles and time is measured in hours. Which car traveled slower? Explain how you know.
Answers
A slower car will travel less distance in the same time.
To know which car traveled slower, we have to compare the distance travelled for the same time, for example t = 3 hours. We can select any time because the speeds are constant (that is why the distance is a proportional function of time).
We can compare them in the graph as:
In the graph we can see that, in 3 hours, car B traveled a longer distance than car A.
Then car A is slower.
Answer: the slower car is car A.
Describe the transformation of f(x)= x2 represented by g. Then graph each function.
Answers
There are two tranformations goinf from f(x) to g(x)
Frist, there is a reflection with respect to the x-axis, which is done by changing the sign of the whole function:
[tex]f_1(x)=-f(x)=-x^2[/tex]Next, to get to g(x), ther is a vertical compression of 2, which is done by dividing the whole function by 2:
[tex]g(x)=\frac{f_1\mleft(x\mright)}{2}=-\frac{1}{2}x^2[/tex]So, to graph it, we can start from f(x):
[tex]f(x)=x^2[/tex]Then reflect and compress like we have done.
We get the function og g(x):
[tex]g(x)=-\frac{1}{2}x^2[/tex]Find the pattern in each sequence and use it to list the next two terms. a. 5, 17, 29, 41, b. 18, 14, 10, 6, c. -9,4,-8,5, -7,6,
Answers
Given:
The objective is to find the pattern and list out the next two terms in the sequence.
Explanation:
a)
The given sequence is 5, 17, 29, 41....
Let's find the difference between the two successive terms of the sequence.
[tex]\begin{gathered} d=17-5=12 \\ d=29-17=12 \\ d=41-29=12 \end{gathered}[/tex]Thus, the common difference between each successive terms is 12.
Then, the next two terms can be calculated as,
[tex]\begin{gathered} 41+12=53 \\ 53+12=65 \end{gathered}[/tex]Hence, the next two terms are 53 and 65.
b)
The given sequence is 18, 14, 10, 6...
Let's find the difference between the two successive terms of the sequence,
[tex]\begin{gathered} d=14-18=-4 \\ d=10-14=-4 \\ d=6-10=-4 \end{gathered}[/tex]Thus, the common difference between each successive terms is -4.
Then, the next two terms can be calculated as,
[tex]\begin{gathered} 6-4=2 \\ 2-4=-2 \end{gathered}[/tex]Hence, the next two terms are 2 and -2.
c)
The given sequence is -9, 4, -8, 5, -7, 6.
Here it can be observed that starting from -9, the alternate numbers are increasing.
Then, the next number can be calculated by find the difference between those sequence provided with alternae places.
[tex]\begin{gathered} d=-8-(-9)=1 \\ d=-7-(-8)=1 \end{gathered}[/tex]Thus, the common difference between each successive terms is 1.
Similarly, the commo difference between the series present inside is,
[tex]\begin{gathered} d=5-4=1 \\ d=6-5=1 \end{gathered}[/tex]Then, the next two number will be,
[tex]\begin{gathered} -7+1=-6 \\ 6+1=7 \end{gathered}[/tex]Hence, the two numbers are -9, 4, -8, 5, -7, 6, -6, 7.
The length of the rectangle is 9 feet and width of the rectangle is three fourths of the length. Which represents the width of the rectangle?
Answers
Explanation
This is the given rectangle:
The width of the rectangle is:
[tex]W=\frac{3}{4}L=\frac{3}{4}\times9[/tex]Answer
The correct answer is option 1: 9 x 3/4
Tickets of a program at college cost $3 for general admission or $2 with a student ID.If 182 people paid to see a performance and $440 was collected, how many ofeach type of ticket were sold?In a program at college ____ tickets were sold for general admission and ____ tickets were sold with a student ID.
Answers
Solution
Given that
This is a system of equations problem.
Let G = the number of general admission tickets and S = the number of student ID tickets.
G + S = 182 Total tickets.
3G + 2S = 440 Total price paid for tickets.
G + S = 182
S = 182 - G
3G + 2S = 440
3G + 2 * (182 - G)= 440
3G + 364 -2G = 440
G = 440 - 364 = 76 General admission tickets
Substitute this into either equation and solve for S.
We already solved one for S symbolically, so we'll use that.
S = 182 - G
S = 182 - 76 = 106 Student ID tickets
In a program at college __76__ tickets were sold for general admission and _106___ tickets were sold with a student ID.
Find the sum and classify the polynomial based on degree and number of terms.
Answers
We need to simplify the given expression as follows:
[tex]\begin{gathered} 3n^2(5n^2-2n+1)+(4n^2-11n^4-9) \\ =(15n^4-6n^3+3n^2)+(4n^2-11n^4-9) \\ =4n^4-6n^3+7n^2-9 \end{gathered}[/tex]Now, to determine the degree of the polynomial we need to find the term which has the biggest exponential term. In this case, it is 4n^4. So, the expression is a 4th-degree polynomial.
Then, the answer is option C. 4th degree polynomial with 4 terms
The letters COCONUT are written on 8 cards. A card is chosen, what is the probability that it will be a letter in the word CHOCOLATE?
Answers
We have the Word COCONUT and the word CHOCOLATE as we can see the common letter in the word are C, O, T
The probability to obtain a letter that in the word Chocolate is
[tex]P(\text{letter in the word chocolate)=P(C)+P(O)+P(T)}[/tex]where
[tex]\begin{gathered} P(C)=\frac{2}{7} \\ P(O)=\frac{2}{7} \\ P(T)=\frac{1}{7} \end{gathered}[/tex]then we substitute this information
[tex]P(\text{letter in the word chocolate)=}\frac{2}{7}+\frac{2}{7}+\frac{1}{7}=\frac{5}{7}[/tex]The probability to chose a card that it will be a letter in the word CHOCOLATE is 5/7
One pump can empty a pool in 3 days, whereas a second pump can empty the pool in 9 days. How long will it take the two pumps, working together, to empty the pool?It will take the two pumps ___days to empty the pool together.If needed, round answer to 3 decimal places.Enter DNE for Does Not Exist, oo for Infinity
Answers
The first pump has a rate of 1/3 a day.
The second pumo has a rate of 1/9 a day.
If both pumps are working together then the total rate is:
[tex]\frac{1}{3}+\frac{1}{9}=\frac{9+3}{27}=\frac{12}{27}[/tex]each day.
Then it will take a total of:
[tex]\frac{27}{12}=2.25[/tex]Therefore it will take the two pumps 2.25 days to emprty the pool together.
The veterinarian weighed Oliver’s new puppy, Boaz, on a defective scale. He weighed pounds. However, Boaz weighs exactly pounds. What is the percent of error in measurement of the defective scale ? Round your answer to the nearest whole number.
Answers
It is given that Boaz weight is 36 pounds on a defective scale and exact weight is 34 pounds.
To determine the percent of error in measurement of the defective scale
[tex]PE=\frac{approxvalue-exactvalue}{\text{exactvalue}}\times100[/tex][tex]PE=\frac{36-34}{34}\times100=\frac{2}{34}\times100=5.882[/tex]Hence the percent error in measurement of the defective scale is 6.
I need you to check if I got it right my answer was 190
Answers
Answer:
190
Explanation:
The volume of a rectangular pyramid is given by
[tex]V=\frac{1}{3}l\times w\times h[/tex]where
L = length of the rectangular base
W = width of the rectangular base
h = heig
how can you figure out how many squares are in figure 50??
Answers
The pattern followed in numbering the squares is such that, each number of squares is added to itself and then two squares are added at the edge of it, one square at either end.
Hence, one square would be
1 = 1 + 1 + 2
2 = 2 + 2 + 2
And so on
This can be expressed in algebraic form as follows;
When x is the number given, the number of squares in it becomes
x = x + x +2
x = 2x + 2
So if x is 50, then the number of squares is now,
x(50) = 2(50) + 2
x(50) = 100 + 2
x(50) = 102
Therefore in figure 50 you have 102 squares.
The number of students per teacher increased the most between ?
Answers
The inclination(also known as the slope) of the line tells us the rate the graph is increasing or decreasing. The biggest increase will correspond to the highest slope, and this happens between 2012 and 2014.
goodmorning, i just need an answer for 1A & 1B , 1c is already answered
Answers
Given:
[tex]g(x)=\frac{1}{4}\sqrt[3]{x-3}+2[/tex]The function represents the number of users in millions who logged into a website since midnight.
1a. How many users have logged in by 9 am?
at 9am x = 9
Substitute x = 9 into g(x)
This gives
[tex]g(9)=\frac{1}{4}\sqrt[3]{9-3}+2[/tex]Simplify the expression
[tex]\begin{gathered} g(9)=\frac{1}{4}\sqrt[3]{3}+2_{} \\ g(9)=\frac{1}{4}\times1.44+2 \\ g(9)=2.36\text{ million} \end{gathered}[/tex]Therefore, 2360000 users have logged into the website by 9 am.
1b Domain and range of the function.
The domain of the function is the set of all input values for which the function is real and defined.
The values of x in g(x) starts from midnight
Hence at midnight x = 0, there are 24 hours in a day
Hence the domain of g(x) is
[tex]\lbrack0,24)[/tex]Range
The range of the function is the set of values of the dependent variables for which a function is defined
Since the function g(x) is defined for all dependent variables x
Then the range of the function is
[tex]\lbrack1.639,2.69)[/tex]The range is in millions
Consider the right triangle shown below.Suppose the hypotenuse of this right triangle is r=7 cm long.Suppose that sin(θ)=0.629.y is how many times as large as r? ____times as large What is the value of y?y=Suppose that cos(θ)=0.778.x is how many times as large as r? ______times as large What is the value of x?x=
Answers
y is 0.629 times as large as r
x is 0.778 times as large as r
y = 4.403
x = 5.446
Explanations:From the right-angled triangle shown:
The opposite is the side facing the angle θ
Opposite = y
The Hypotenuse is the longest side of the triangle
Hypotenuse = r
The Adjacent is the third side
Adjacent = x
Suppose sinθ = 0.629
r = 7
[tex]\begin{gathered} \sin \theta\text{ = }\frac{Opposite}{\text{Hypotenuse}} \\ 0.629\text{ = }\frac{y}{r} \\ 0.629\text{ = }\frac{y}{7} \\ y\text{ = 7(0.629)} \\ y\text{ is 0.629 times as large as r} \\ y\text{ = }4.403 \end{gathered}[/tex]Suppose that cos θ = 0.778
and r = 7
[tex]\begin{gathered} \cos \theta\text{ = }\frac{Adjacent}{\text{Hypotenuse}} \\ 0.778\text{ = }\frac{x}{r} \\ 0.778\text{ = }\frac{x}{7} \\ x\text{ = 0.778(7)} \\ x\text{ is 0.778 times as large as r} \\ x\text{ = }5.446 \end{gathered}[/tex]8rs - 8s= 16p solve for r.
Answers
Given data
8rs - 8s = 16p
Required
Solve for s
Step 1
Move 8s to the right-hand side of the equation
8rs =16p + 8s
Step 2
Divide both sides by s
(8rs/s)=(16p + 8s)/s
8r = 16p/s + 8
Step 3
Divide both sides by 8
8r/8 = (16p/s)/8 +8/8
r = (16p/s) x (1/8) + 1
r = (2p/s) + 1
if jaden drove 40 miles how many gallons of gas would be left in the tank
Answers
The x axis of the graph show the distance driven and y axis represnt Gas remains
at 40 miles of distance i.e x =40
Then value of y at x = 40 is 3.5 i.e. y = 3.5
Write an equation that describes the following relationship: y varies inversely as the cube root of x and when x=64, y=2
Answers
Since y varies inversely as the cube root of x then:
[tex]\begin{gathered} y=\frac{k}{\sqrt[3]{x}}, \\ \text{where k is the constant of proportionality.} \end{gathered}[/tex]Now, to determine the value of k, we use the fact that when x=64, y=2:
[tex]2=\frac{k}{\sqrt[3]{64}}.[/tex]Solving the above equation for k we get:
[tex]\begin{gathered} \frac{k}{\sqrt[3]{64}}\times\sqrt[3]{64}=2\times\sqrt[3]{64}, \\ k=2\sqrt[3]{64}, \\ k=2\cdot4=8. \end{gathered}[/tex]Therefore:
[tex]y=\frac{8}{\sqrt[3]{x}}\text{.}[/tex]Answer:
[tex]y=\frac{8}{\sqrt[3]{x}}\text{.}[/tex]Find the length of the segment that starts at (3,4)and goes to (8,7).
Answers
To find the length of a segment delimited by two points we need to find the distance between said points. This is done by using the following expression:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]We then need to apply the coordinates of the given points:
[tex]\begin{gathered} d=\sqrt[]{(8-3)^2+(7-4)^2} \\ d=\sqrt[]{5^2+3^2} \\ d=\sqrt[]{25+9=\sqrt[]{36}} \\ d=6 \end{gathered}[/tex]The segment has a length of 6 units.
What is the distance from point P(- 1, 1) to the line y = -2x + 4? Round to the nearest tenth.
Answers
Line equation: y = -2x + 4, Point (-1,1)
We have to write the equation in the standard form:
y = -2x + 4
-2x - y + 4 = 0
Now we can see the values of a, b, c and x0 and y0 to use the formulas
a = -2
b = -1
c = 4
x0 = -1
y0 = 1
Distance = abs(ax0 + by0 + c)/sqrt(a^2 + b^2) = abs(-2(-1) -1 (1) + 4)/sqrt((-2)^2 + (-1)^2) =
D = abs(2 - 1 + 4)/sqrt(4 + 1) = abs(5)/sqrt(5) = 5/2.236067 = 2.2360
Rounding to nearest tenth: Distance = 2.2
Answer: Distance is 2.2
[tex]d\text{ = }\frac{\mathrm{abs}(ax_0+by_0+c)}{\sqrt[]{a^2+b^2}}[/tex]2,070 people attended the afternoon showing and 1,500 people attended the evening showing of the play Aladdin in total each day during a 6-day run. How many tickets were sold each day for both the afternoon and evening performances all together? (the same amount were sold each day)
Answers
2,070 people attended the afternoon showing and 1,500 people attended the evening showing of the play Aladdin in total each day during a 6-day run. How many tickets were sold each day for both the afternoon and evening performances altogether? (the same amount were sold each day)
Let
x -----> number of tickets sold each day (afternoon)
y ----> number of tickets sold each day (evening)
Divide the total tickets by the number of days
x=number of tickets sold each day (afternoon)=2,070/6=345y=number of tickets sold each day (evening)=1,500/6=250supposed charity received a donation of 24.1 million dollars if this represents 37% of the Charities donated funds what is the total amount of its funds round your answer to the nearest million dollars.
Answers
Given,
24.1 million dollars = 37% of total
We let "x" be the total. So we can say:
37% of x is 24,100,000
We can translate this into an equation [of means multiplication and is means equals]:
[tex]\begin{gathered} 0.37\cdot x=24,100,000 \\ \end{gathered}[/tex]Note: 37% is 37/100 = 0.37
Now,
We solve this equation for x [total amount]:
[tex]\begin{gathered} 0.37\cdot x=24100000 \\ x=\frac{24100000}{0.37} \\ x=65135135.1351 \end{gathered}[/tex]That is:
65,135,135.1351
Rounded to nearest million:
65,000,000 [65 million]
0.6(x-2)=0.3x+5-0.1x
Answers
First, we have to use the distributive property.
[tex]\begin{gathered} 0.6(x-2)=0.3x+5-0.1x \\ 0.6x-1.2=0.3x+5-0.1x \\ \end{gathered}[/tex]Then, we reduce like terms.
[tex]0.6x-1.2=0.2x+5[/tex]Now, we subtract 0.2x from each side.
[tex]\begin{gathered} 0.6x-0.2x-1.2=0.2x-0.2x+5 \\ 0.4x-1.2=5 \end{gathered}[/tex]Then, we add 1.2 on each side.
[tex]\begin{gathered} 0.4x-1.2+1.2=5+1.2 \\ 0.4x=6.2 \end{gathered}[/tex]At last, we divide both sides by 0.4.
[tex]\begin{gathered} \frac{0.4x}{0.4}=\frac{6.2}{0.4} \\ x=15.5 \end{gathered}[/tex]Therefore, the solution to the equation is x = 15.5.Which transformation can NOT be used to prove that ABC is congruent toA DEF?ÁO A. rotationB. reflectionC. dilationD. translation
Answers
If two triangles are congruent, it means that the lengths of their corresponding sides and angles are equal. Thus, the triangles have equal sizes. Transformations involing rotation, reflection and translation does not change the size of the triangle but dilation does. It increases or decreases it. Thus, the correct option is
C. dilation