Okay, here we have this:
Considering the provided information, we are going to calculate how many messages did they each send, so let's solve the following equation (where x represents the number of messages sent by Josh):
[tex]\begin{gathered} 4x+(10+x)+x=160 \\ 6x+10=160 \\ 6x=150 \\ x=\frac{150}{6} \\ x=25 \end{gathered}[/tex]Then, we have that:
Number of text messages Chang sent= 4x= 4*25=100
Number of text messages Martina sent= 10+x = 10 + 25 = 35
Number of text messages Josh sent= x= 25
Translate and simplify: the quotient of -25 and the sum of c and d.Provide your answer below:
Use algbraic languaje to write the given expression.
The quotient between two expressions A and B can be written as:
[tex]\frac{A}{B}[/tex]On the other hand, the sum of c and d can be expressed as:
[tex]c+d[/tex]Then, the quotient between -25 and the sum of c and d is the same as the quotient of -25 and c+d:
[tex]\frac{-25}{c+d}[/tex]Therefore, the answer is:
[tex]\frac{-25}{c+d}[/tex]Find the volume of the rectangular pyramid. A) 480 in^3B) 160 in^3C) 1,440 in^3D) 48 in^3
From the given rectangular pyramid, we have the following dimensions:
• Length, L = 10 in
,• Width, w = 6 in
,• Height, h = 8 in
Let's find the volume of the rectangular pyramid.
To find the volume of the rectangular pyramid, apply the formula:
[tex]V=\frac{l*w*h}{3}[/tex]Where V is the volume.
Substitute values into the formula and solve for V:
[tex]\begin{gathered} V=\frac{10*6*8}{3} \\ \\ V=\frac{480}{3} \\ \\ V=160\text{ in}^3 \end{gathered}[/tex]Therefore, the volume of the rectangular pyramid is 160 cubic inches.
ANSWER:
160 in³
find the simple interest earned, to the nearest cent, for each principal, interest rate, and time.$750 - 7% - 3 years
We have to apply the simple interest formula:
I = p x r x t
Where :
I = interest
p = principal amount
r= interes rate ( in decimal form, percentage divided by 100)
t= time (years)
Replacing with the values given:
I = 750 x (7/100) x 3
I = 750 x 0.07 x 3
I = $157.7
If there are 90 students in Jazz Band and 5/6 of them are in 8th grade, how many 8th graders are in Jazz Band?
Given,
The number of total student in the band are 90.
The part of the total student from 8th grade is 5/6.
The number of grade 8th students are,
[tex]\begin{gathered} \text{Number of grade 8th student }=\frac{5}{6}\times90 \\ \text{ = }5\times15 \\ \text{ = 75} \end{gathered}[/tex]The number of students in the band from grade 8th is 75.
Hence, 75 are 8th grader are in jazz band.
Estimation Gabe goes to the mall. If k is the number of items he bought, the exp11.02k +21 gives the amount he spent in dollars at one store. Then he spent 30 dollars at anotherstore. Find the expression which represents the amount Gabo spent at the mall. Then estimatehow much Gabe spent if he bought 2 items.What expression represents the amount in dollars that Gabe spent at the mall?
The expression 11.02k+21 indicates how much did Gabe spend in the first store he visited.
In the second store, he spent 30 dollars.
To determine how much he spent in the mall you have to add the amounts he spent in both stores:
[tex]\begin{gathered} \text{Store}1+\text{Store}2 \\ (11.02k+21)+30 \\ 11.02k+21+30 \\ 11.02k+51 \end{gathered}[/tex]The expression that represents his total expenses at the mall is
[tex]11.02k+51[/tex]"k" represents the number of items he bought. If he bought k=2 items, you can calculate how much he spent at the mall as follows:
[tex]\begin{gathered} 11.02k+51 \\ 11.02\cdot2+51 \\ 72.04 \end{gathered}[/tex]Gabe spent an estimate of 72.04 dollars at the mall
6. Is 9,738 divisible by 9? If it is, write the number as the product of 9 and another factor. If not, explain.
I need to find the weight of the cast iron shape
Density of iron:
[tex]0.2607\frac{lb}{in^3}[/tex]Then the weight of the cast iron shape is given by 0.2607*V, whe V is its volume.
The volume of the cast iron shape is given by its base area multiplied by its height. Since its base has the form of an equilateral triangle with side length of 4 in, its area is . Then we have:
[tex]\begin{gathered} V=4\sqrt[]{3}\cdot6=24\sqrt[]{3}\approx41.6in^3 \\ \text{Therefore, the weight is:} \\ 0.2607\cdot24\sqrt[]{3}=10.8\text{ }lb \end{gathered}[/tex]Simplify.12(3x + 5y)36 x + 60 y96 - 8 p36 x + 5 y96 xy
1) We can simplify this by applying the Distributive property, a.k.a FOIL.
[tex]\begin{gathered} 12(3x+5y) \\ 12\cdot3x+12\cdot5y \\ 36x+60y \end{gathered}[/tex]2) Thus, we can tell that when we expand this expression, we get a simpler one and this is:
[tex]36x+60y[/tex]2-4 AdditionalMultimediaIn 1-10, write the ordered pair for each point.1. A (-8,6)2. B(2,2)1084. D3.C (-3,-6)00(8,-8)AF65. € (-7,-9)6.F (6,6)G7.6 (-6,3)8. HB(4,-4)29.1(9,0)10.)(0,4)F10 -8 -6 -4 -2 O22.4668102HIn 11-16, graph and label each point.11. U(-5, -3)12. V-9,3)-44c-613. W(38)14. X(8,3)DCOE1015. Y(6, -6)16. Z(-5,0)In 17-25 write the ordered pair for each point
#12.
The point to be plotted is: V(- 9, 3)
This means that x = - 9 and y = 3 at point V.
This implies that we must count 9 units on the x-axis. We count in the negative direction of the x-axis because -9 is a negative number.
Also, we must count 3 units on the y-axis in the positive direction.
Now, we can plot this on a graph like this:
what is the equation in slope- intercept form of the line that passes through the points (-26 -11) and (39, 34) ?A) y = -9/13 x + 7 B) y = -9/13 x - 7 C) y = 9/13 x + 7 D) y = 9/13 x - 7
what is the equation in slope- intercept form of the line that passes through the points (-26 -11) and (39, 34) ?
A) y = -9/13 x + 7
B) y = -9/13 x - 7
C) y = 9/13 x + 7
D) y = 9/13 x - 7
step 1
Find out the slope
m=(34+11)/(39+26)
m=45/65
simplify
m=9/13
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=9/13
point (39,34)
substitute and solve for b
34=(9/13)(39)+b
b=34-27
b=7
therefore
the equation is
y=(9/13)x+7
option CFind the center of the circle with a diameter that has endpoints (−10,10) and (5,−8) .
to find the center, we need to find the midpoint between these two points, the equation is:
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]so in this case:
[tex]\begin{gathered} (\frac{-10+5}{2},\frac{10-8}{2}) \\ (\frac{-5}{2},1)\text{ or (-2.5,1)} \end{gathered}[/tex]so the answer is: the center is in (-2.5,1)
4 Select the correct answer from each drop-down menu. Consider the function shown on the graph. y 8-4 8 6 6 NO o →X 12 N 2 글 6 8 10 2 4 -6- 003 Complete the statements to make them true. function. This is the graph of a The x-intercept of the function is at Reset Next
The graph of a function is a square root function.
When you draw the standard square root function in the desmos , you will get the same square root curve as it is given in the question.
Therefore the graph of a function is a square root function.
In second part , we have to determine the x-intercept of the function.
The x-intercept of the function is that where the y-coordinate is equal to zero.
In the graph , the coordinates where y-coordinate is 0 at
[tex](8,0)[/tex]Sales (Y) Temperature (X) 100 92 213 88 830 54 679 62 209 85 189 16 1110 52 456 65 422 68 235 89 199 91
Given:
We are provided with the data of X(temperature), sales(y)
Required:
We have to draw the graph for given data.
Explanation:
We are going to draw a graph in 2-d in which x axis represent temperature.
While y axis represent sales.
We are going to place value in the graph and draw the line at given points.
X-axis represent temperature.
Y-axis represent sales.
Required answer:
Above graph is our answer,
the volume of a sphere is 972 π , find the radius of the sphere
To determine the radius of a sphere
angle is 105 (3x-15) 1. x=402.x=1053.x=54.x=30
angle is 105
(3x-15) =105
solve for x
3x=105+15
3x=120
x=120/3
x=40
answer is
Find the mean. If necessary, round to one decimal place60, 57, 86, 26, 128, 82
1) We need to add them up over the number of data points. By doing this we can write out the following:
[tex]\bar{x}=\frac{60+57+86+26+128+82}{6}=\frac{439}{6}\approx73.2[/tex]Note that we don't need to write the data points in order to find the mean.
Thus, the answer is 73.2 (to the nearest tenth)
Find: a. f(0)b. f(3) c. f(-5) d. x when f(x)=2e. x when f(x)=0
Question:
Find:
a. f(0)
b. f(3)
c. f(-5)
d. x when f(x)=2
e. x when f(x)=0
Solution:
Taking into account the previous graph, we can say that:
f(0) = 0
f(3) = 1.7 (approximately)
f(-5) = 0
x= 0.7 (approximately) when f(x) = 2
x = 0 or x =-5 when f(x)= 0
1. Which of the following is NOT a characteristic of t-distribution?A. Like the normal distribution, the t-distribution has a smooth shape.B. Like the normal distribution, the t-distribution is symmetric. If you think about folding it in half at the mean, each side will be the same.C. Like a standard normal distribution (or z-distribution), the t distribution has a mean of one.D. The normal distribution assumes that the population standard deviation is known. The t-distribution does not make this assumption.
The t-distribution can be seen in the following image:
As you can see, like the normal distribution, the t-distribution has a smooth shape, they are also symmetric. They mean of both distributions is 0.
Also, the t-distribution does not make the assumption that the population standard deviation is known.
Therefore, from the given options the one that is not a characteristic of t-distribution is option C, because the mean of the t-distribution is 0, not 1 as the option says.
Directions: Solve each equation. Check your solution(s) then indicate whether or not the solutions are extraneous. 1. 12x + 12) = 4x 2. 3x - 2) = 10 Week 16. Homework Packet 2 MB VIEW
Given the equation :
[tex]|2x+12|=4x[/tex]So,
[tex]\begin{gathered} 2x+12=4x\text{ OR -(2x+12)=4x} \\ \end{gathered}[/tex]For the first possible solution :
[tex]\begin{gathered} 2x+12=4x \\ 12=4x-2x \\ 12=2x \\ \\ x=\frac{12}{2}=6 \end{gathered}[/tex]For the second possible solution:
[tex]\begin{gathered} -(2x+12)=4x \\ -2x-12=4x \\ -12=4x+2x \\ -12=6x \\ \\ x=-\frac{12}{6}=-2 \end{gathered}[/tex]So, the answer is : x = 6 or x = -2
Note: the solution is extraneous because for the case if x = -2
The right side will be equal 4 * -2 = -8, and this is not logic because the output of the absolute value must be positive
Theo wants to use a cookierecipe that makes 36 cookies but hewants to reduce the number of cookiesto 24. If the recipe specifies using2 cups of sugar, how much sugar shouldhe use?
First, we have to find the ratio of the number of cookies that Theo wants to cook to the number of cookies that the recipe establishes, since the original number of cookies is 36 and the number of cookies wanted is 24, we get:
[tex]\frac{24}{36}=\frac{2}{3}[/tex]Now that we got the fraction 2/3, we just have to multiply it by the amount of sugar originally established by the recipe, this way we get the amount of sugar that he needs to prepare 24 cookies:
[tex]\frac{2}{3}\times2=\frac{4}{3}[/tex]Or as a mixed number:
[tex]\frac{4}{3}=1\frac{1}{3}[/tex]Then, he should use 1 1/3 cups of sugar (4/3)
I'm stuck on this question, I have to solve for "e"
Given the following equation shown in the picture:
[tex]\frac{E}{e}=\frac{R+r}{r}[/tex]You can solve for the variable "e" by following the steps shown below:
Step 1. You must apply the Multiplication property of equality by multiplying both sides of the equation by "e". As you can see below:
[tex]\begin{gathered} (e)(\frac{E}{e})=(e)(\frac{R+r}{r}) \\ \\ E=\frac{e(R+r)}{r} \end{gathered}[/tex]Step 2. Now you must apply the Multiplication property of equality again by multiplying both sides of the equation by "r":
[tex]\begin{gathered} (r)(E)=(r)(\frac{e(R+r)}{r}) \\ \\ Er=(1)e(R+r) \\ Er=e(R+r) \end{gathered}[/tex]Step 3. Finally, apply the Division property of equality by dividing both sides of the equation by:
[tex](R+r)[/tex]Then, you get:
[tex]\begin{gathered} \frac{Er}{(R+r)}=\frac{e(R+r)}{(R+r)} \\ \\ \frac{Er}{R+r}=e \end{gathered}[/tex]Therefore, the answer is:
[tex]e=\frac{Er}{R+r}[/tex]victor needs 300 feet of rope.The rope he wants to buy is sold by yards.He knows that there are 3 feet in 1 yard.How many yards should he buy?Explain how u got this answer
We need to convert 300 feet to yards.
We know,
3 feet = 1 yard
Hence,
300 feet * 1 yard/3 feet = 300/3 = 100 yards
He should buy 100 yards
47) Two triangles are similar, and the ratio of eachpair of corresponding sides is 2 : 1. Whichstatement regarding the two triangles is NOTtrue? ?A. Their areas have a ratio of 4 : 1.B. Their altitudes have a ratio of 2 : 1.C. Their perimeters have a ratio of 2 : 1.D. Their corresponding angles have a ratio of 2 : 1.
D
1) Two triangles are similar if their sides are proportional to each other and their angles are congruent.
2) If the ratio is 2:1 then the larger triangle is twice larger than the other one.
3) Examining the options we can state that their corresponding angles do not have a ratio of 2:1. So this is false. And the answer is D
A rectangular tank measuring 18m by 6m is 2/3 filled with water.if the water is poured into another rectangular tank which is 12m long and 10m wide, what will be the height of the water level in the second tank?
Solution
Step 1
Write an expression for the volume of a cuboid
[tex]\text{Volume of cuboid = L}ength\text{ }\times width\times height[/tex]Step 2
Find the volume of the first rectangular tank
[tex]\text{Volume of first tank =}18m\text{ }\times18m\times\frac{2}{3}\times6m=1296m^3\text{ }[/tex]Step 3
Find the volume of the second tank
[tex]\text{Volume of second tank = 12m }\times10m\times height[/tex]Step 4
Equate both volumes
[tex]\begin{gathered} 1296\text{ = 120}\times height \\ \text{height of water in second tank = }\frac{1296}{120}=10.8m \end{gathered}[/tex]Height of second rectangular tank = 10.8m
pets : | bird | cat | dog | snake | _____________________________relative frequency: | 3 | 5 | 11 | 1 |which information best completes a relative frequency table about the pets at the farm?a. pets : | bird | cat | dog | snake | _____________________________ relative frequency: | 0.20 | 0.25| 0.45 | 0.10 |b. pets : | bird | cat | dog | snake | _____________________________relative frequency: | 0.15 | 0.20| 0.55 | 0.10 |c. pets : | bird | cat | dog | snake | _____________________________relative frequency: | .15 | .25 | .55 | .05 |d. pets : | bird | cat | dog | snake | _____________________________relative frequency: | .15 | .20 | .6 | .05 |
ANSWER :
C. bird = 0.15
cat = 0.25
dog = 0.55
snake = 0.05
EXPLANATION :
From the problem, we have the following frequencies :
bird = 3
cat = 5
dog = 11
snake = 1
The total number of animals is 3 + 5 + 11 + 1 = 20
The relative frequency formula is :
[tex]\text{ Relative Frequency}=\frac{\text{ Frequency \lparen Number per animal\rparen}}{\text{ Total number of Frequency \lparen Total number of animals\rparen}}[/tex]That will be :
[tex]\begin{gathered} \text{ Bird}=\frac{3}{20}=0.15 \\ \\ \text{ Cat}=\frac{5}{20}=0.25 \\ \\ \text{ Dog}=\frac{11}{20}=0.55 \\ \\ \text{ Snake}=\frac{1}{20}=0.05 \end{gathered}[/tex]Hello! I really need help with creating and solving this problem.
EXPLANATION:
Required;
We are required to create two data sets, each with 7 data points and a mean of 10.
Also, to draw a box plot for the data set.
Step-by-step solution;
We shall randomly take 7 numbers whose sum is 70. We know that 70 divided by 7 is 10, therefore the average for these 7 numbers is already known as required.
The data set therefore would be;
PART A:
[tex]5,8,10,11,11,12,13[/tex]The mean shall be;
[tex]\begin{gathered} Mean=\frac{5+8+10+11+11+12+13}{7} \\ \\ Mean=\frac{70}{7} \\ \\ Mean=10 \end{gathered}[/tex]The box plot would now appear as follows;
PART B:
[tex]4,8,9,9,13,11,16[/tex]The mean shall be;
[tex]\begin{gathered} Mean=\frac{4+8+9+9+11+13+16}{7} \\ \\ Mean=\frac{70}{7} \\ \\ Mean=10 \end{gathered}[/tex]The box plot would now appear as follows;
John bought a machine to make fresh juice. He has five different fruits: strawberries,oranges, apples, pineapples, and lemons. If he only uses two fruits, how many differentjuice drinks can John make?
Given:
Total number of fruits John bought is 5.
John chooses 2 fruits to make a juice.
[tex]\begin{gathered} \text{Number of ways that John make Juice=5C}_2 \\ \text{Number of ways that John make Juice=}\frac{5\times4}{1\times2} \\ \text{Number of ways that John make Juice=}10 \end{gathered}[/tex]10 different juice drinks can John make.
Van said, "The expression y-r is equivalent to the expression -(x - y)." Do you agree with Van? A. Agree, because – in front of the parentheses means to use the Distributive Property to multiply by -1. Then use the Commutative Property. B. Agree, because – in front of the parentheses means to subtract everything in the parentheses, which changes the signs. Then, use the Commutative Property. C. Disagree, because the order of the variables cannot be changed with subtraction. D. Disagree, because it depends on the value of the variables. Ο Α B с OD
ANSWER:
C. Disagree, because the order of the variables cannot be changed with subtraction.
STEP-BY-STEP EXPLANATION:
We operate the expression and we are left with
[tex]y-x=-(-y+x)[/tex]Write an equation for each equation of y=|x| 6 units left A. Y=|x| -6 B. Y=|x-6| C. Y=|x| + 6 Y=|x+6|
You need to remember the following Transformation rules for functions:
1. When:
[tex]f(x+h)[/tex]The function is shifted left "h" units.
2. When:
[tex]f(x-h)[/tex]The function is shifted right "h" units.
In this case you have the following function:
[tex]y=|x|[/tex]If the function is translated (or shifted) 6 units left, you can identify that the transformation will have this form:
[tex]f(x+h)[/tex]Where:
[tex]h=6[/tex]Then, the equation of this function is:
[tex]y=|x+6|[/tex]The answer is: Last option.
How many 1/3s are in 2? Your answer
6
Explanations:To know the number the number of 1/3 s in 2, we are going to divide 2 by 1/3
[tex]2\div\frac{1}{3}[/tex]This will furtherbe simplified as:
[tex]\begin{gathered} 2\times\frac{3}{1} \\ 2\text{ }\times3\text{ = 6} \end{gathered}[/tex]There are six 1/3 s in 2