Since Johnny bought 15 cookies for 9 dollars, we have that:
[tex]\frac{9}{15}=\frac{3}{5}=0.6[/tex]Therefore, each cookie costs 60 cents
Justine correctly multiplied the decimals shown. How can the product be correct without three decimal places? 8.5 x 2.34 = 19.89. How can the product be correct without three decimal.
8.5 x 2.34 = 19.890 ........ this in three decimal places
without 3 decimal places we must approximate the product to the nearest whole number this is equivalent to 20
A payday loan company charges a $30 fee for a $650 payday loan that will be repaid in 12 days. Treating the fee as interest paid, what is the equivalent annual interest rate?
30.41%
Explanation
Step 1
find the interest for the 12 days
[tex]\begin{gathered} 650\Rightarrow100\text{ percent} \\ 30\Rightarrow x \\ \frac{650}{100}=\frac{30}{x} \\ \\ 650\cdot x=30\cdot100 \\ x=\frac{3000}{650} \\ x=4.61\text{ \% } \end{gathered}[/tex]it means will pay a rate of 4.61% in 12 days
Step 2
we have the interest for 12 days, if we treat the fee as interest paid, the annual interest rate is
[tex]\begin{gathered} \text{Interest rate=365days/12days} \\ \text{Interest rate=30.41 \% } \end{gathered}[/tex]I hope this helps you
let g(x) = 3x+2 and f(x)= (x-2)/3. Find the value. f(g(0))a) 0b) -2/3c) 1d) -1
We have two functions:
[tex]\begin{gathered} g\mleft(x\mright)=3x+2 \\ f\mleft(x\mright)=\frac{x-2}{3} \end{gathered}[/tex]We have to calculate f(g(0)).
We can do it like this:
[tex]\begin{gathered} f(g(0))=\frac{g(0)-2}{3} \\ f(g(0))=\frac{\lbrack3(0)+2\rbrack-2}{3} \\ f(g(0))=\frac{0+2-2}{3} \\ f(g(0))=\frac{0}{3} \\ f(g(0))=0 \end{gathered}[/tex]Answer: a) 0
Which of the two triangles has an area of 68 square units?
Given data:
The given area is A=68 square units.
The area of the first triangle is,
[tex]\begin{gathered} A_1=\frac{1}{2}(17)(8) \\ =68 \end{gathered}[/tex]The area of the second triangle is,
[tex]\begin{gathered} A_2=\frac{1}{2}(8)(15) \\ =60 \end{gathered}[/tex]Thus, the first triangle has an area 68 square-u
find the vertex of each quadratic function by completing the square
We can see that
[tex](x+2)^2=x^2+4x+4[/tex]By comparing this expression with our quadratic function, we get
[tex]y\questeq x^2+4x+4-4-16[/tex]where we added and substracted 4, which gives zero. Now, we can write
[tex]\begin{gathered} y=(x+2)^2-4-16 \\ y=(x+2)^2-20 \end{gathered}[/tex]Now, the quadratic function in vertex form is given by
[tex]y=a(x+h)^2+k[/tex]where the point (h,k) is the vertex. By comparing our last result and this expression, we can see that h=2 and k=-20. Then, the vertex is at point (2,-20).
I need help on net force like if they are pointing eachother do I add it? and how will I know what direction it will move and if it’s unbalanced?
Answer:
Step-by-step explanation:
Use the distributive property to remove the parentheses. 6(4-w)
Problem: Use the distributive property to remove the parentheses.
6(4-w)
Solution:
[tex]6(4-w)\text{ = (6)(4) - 6w}[/tex]this is equivalent to :
[tex]\text{= 24 - 6w }[/tex]then, we have that the correct solution would be:
[tex]6(4-w)\text{ = }24-6w[/tex]What is the value of the expression below? 8113 O A. C B. 3 C. 4 D. 2
We have that
[tex]8^{\frac{1}{3}}=\text{ }\sqrt[3]{8}\text{ = }\sqrt[3]{2^3}\text{ = 2}[/tex]The answer is 2
Tyler built 4/6 of his house in 3/4 of a year. How long will it take him to finish building his house?
Let's begin by listing out the given information:
Tyler built (b) = 4/6
Time (t) = 3/4 year
Tyler complete building (c) = 1
Total time (T) =
It will take thi
the area of square is 49m2.what is the length of one side
Consider that the area (A) of a square with side 's' is given by the formula,
[tex]A=s^2[/tex]Given that the area is 49 sq. meters,
[tex]A=49[/tex]Substitute the values and solve for the side 's' as follows,
[tex]\begin{gathered} s^2=49 \\ s=\sqrt[]{49} \\ s=\pm7 \end{gathered}[/tex]But 's' is the side of the square, which cannot be negative.
So we have to neglect the negative value, and consider the positive value,
[tex]s=7[/tex]Thus, the side of the given square is 7 meters .
A data set consists of these points: (2, 4), (4,7), (5, 12). Malinda found theregression equation to be 9 = -2.5x - 1.5. Is she correct?OA. No. Both a and b are incorrect.OB. No. The value for bis incorrect.OC. No. The value for a is incorrect.OD. Yes. This is the correct equation.
Solution
[tex]y=-2.5x-1.5[/tex]Let us test each of the coordinates points
at ( 2, 4 )
at x=2
[tex]\begin{gathered} y=-2.5(2)-1.5 \\ y=-6.5 \end{gathered}[/tex]No agreement with the y-coordinate
Let us test the second coordinate point ( 4 , 7 )
at x = 4
[tex]\begin{gathered} y=-2.5(4)-1.5 \\ y=-11.5 \end{gathered}[/tex]No agreement with the y-coordinate
Let us test the third coordinate point (5, 12 )
at x= 5
[tex]\begin{gathered} y=-2.5(5)-1.5 \\ y=-14 \end{gathered}[/tex]No agrement with the y-coordinate
Based on the information you have provided in the question , y= - 2.5x - 1.5 is not a correct regression equation for the line .
Sam deposits $2,500.00 into a retirement annuity at the age of 18 and plans to withdraw the money for retirment at the age of 65. The annuity Interest rate is 6.75% interest, compounded monthly. What is the ending balance?
The ending balance is 59,139.60
Here, we want to find the balance for a retirement account in which the initial deposit is compounded monthly at a certain percentage
Mathematically, we proceed to use the compound interest formula ;
[tex]\begin{gathered} A\text{ = P(1 + }\frac{r}{n})^{nt} \\ \\ \text{where A is the balance we want to calculate} \\ \\ P\text{ is the amount deposited which is 2,500} \\ \\ r\text{ is the annual interest rate which is 6.75\% which is 0.0675} \\ \\ n\text{ is the number of times the interest is componded yearly} \\ At\text{ a monthly rate, we have 12 times per year} \\ \\ t\text{ is the number of years which is 65-18 = 47} \end{gathered}[/tex]So, we proceed to insert these values;
[tex]\begin{gathered} A\text{ = 2500( 1 + }\frac{0.0675}{12})^{12\times47} \\ \\ A=2500(1+0.005625)^{564} \\ \\ A=2500(1.005625)^{564} \\ \\ A\text{ = 59,139.60} \end{gathered}[/tex]Slope intercept formPlease Solve everything with the exception of 8
The equation of a line in slope intercept form is in the form,
[tex]y=mx+c[/tex]SOLUTION
3) 2y - 6 = -6x
Add 6 to both sides
[tex]\begin{gathered} 2y-6+6=-6x+6 \\ 2y=-6x+6 \end{gathered}[/tex]Divide through by 2
[tex]\begin{gathered} \frac{2y}{2}=-\frac{6x}{2}+\frac{6}{2} \\ y=-3x+3 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-3x+3[/tex]4) - 11x - 7y = -56
Add +11x to both sides
[tex]\begin{gathered} -11x-7y+11x=-56+11x \\ -7y-11x+11x=11x-56 \\ -7y=11x-56 \end{gathered}[/tex]Divide both sides by - 7
[tex]\begin{gathered} \frac{-7y}{-7}=\frac{11x}{-7}-\frac{56}{-7} \\ y=-\frac{11x}{7}+8 \end{gathered}[/tex]Hence, the equation in the slope intercept form is
[tex]y=-\frac{11x}{7}+8[/tex]Do you no the answer to this f(x)=4x^2-17x+3Solve for the values of x
Answer:
[tex]x=\frac{17+\sqrt[]{241}}{8},\frac{17-\sqrt[]{241}}{8}[/tex]Explanation:
Given the below function;
[tex]f(x)=4x^2-17x+3[/tex]Note that a quadratic equation in standard form is generally given as;
[tex]y=ax^2+bx+c[/tex]If we compare both of the equations above, we can deduce that;
[tex]a=4,b=-17,c=3[/tex]We'll now use the below quadratic formula to solve for the values of x as seen below;
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{17\pm\sqrt[]{(-17)^2-4\cdot4\cdot3}}{2\cdot4} \\ x=\frac{17\pm\sqrt[]{289-48}}{8} \\ x=\frac{17\pm\sqrt[]{241}}{8} \\ \therefore x=\frac{17+\sqrt[]{241}}{8},\frac{17-\sqrt[]{241}}{8} \end{gathered}[/tex]
A spice rack has 6 shelves. Each shelf can display 15 spice jars. How many spice racks does a store need to display 2,250 spice jars?
We have
1 spice rack ----- 6 shelves
1 shelf ---- 15 spice jar
First, we need to know the number of shelves, so we will divide 2250 between 15
[tex]\frac{2250}{15}=150[/tex]We will need 150 shelves for 2250 spice jars
Then we need to know the number of spice racks, so we need to divide 150 between 6
[tex]\frac{150}{6}=25[/tex]We will need 25 spice racks for 2250 spice jars
find the rate of change represented in each table or graph
ANSWER
[tex]-\frac{1}{2}[/tex]EXPLANATION
We want to find the rate of change of the graph given.
To do this, we apply the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1, y1) and (x2, y2) are two points on the line.
From the given graph, let us pick the points (-1, -3) and (3, -5).
Therefore, the rate of change of the graph is:
[tex]\begin{gathered} m=\frac{-5-(-3)}{3-(-1)}=\frac{-5+3}{3+1} \\ m=\frac{-2}{4} \\ m=-\frac{1}{2} \end{gathered}[/tex]That is the rate of the change of the graph.
A random sample of n= 100 observations is selected from a population with u = 29 and o = 25. Approximate the probabilities shown below.b. P(22.1 ≤ x ≤ 26.8) (Round to three decimal places as needed.)
To be able to get the probability of a certain value to be selected, we need to convert it to a z-score or z-value. To convert that, we have the formula below:
[tex]z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt[]{n}}}[/tex]where:
bar x = sample mean
μ = population mean = 29
σ = population standard deviation = 25
n = sample size = 100
So, let's start determining the probabilities between 22.1 and 26.8 mean values.
x = 22.1
[tex]z=\frac{22.1-29}{\frac{25}{10}}=\frac{-6.9}{2.5}=-2.76[/tex]x = 26.8
[tex]z=\frac{26.8-29}{2.5}=\frac{-2.2}{2.5}=-0.88[/tex]Let's plot these values to the normal curve with their corresponding areas. The corresponding areas can be found using the Z Normal Distribution.
As you can see in the graph above, the area covered from 0 to -0.88 is 0.3106 while the area covered from 0 to -2.76 is 0.4971.
To get the area covered from -0.88 to -2.76, we need to subtract the two.
[tex]0.4971-0.3106=0.1865\approx0.187[/tex]Therefore, the area covered between x = 22.1 and x = 26.8 is approximately 0.187.
How to Use the Z-Table:
The above picture shows the area from 0 to 0.88. We have 0.8 as our row and 0.08 as our column. The intersection of this row and column is our area for 0.88 from the center of our normal curve. In this case, we have 0.3106.
Another example: The area to the left of -0.32 or z ≤ -0.32.
In the figure above, the area to the left of -0.32 is the one colored in green. The red area is the area from -0.32 to the center 0 which is 0.1255.
Remember, the area from the center of the normal curve is 0.5. If the red area is already 0.1255, how much is left for the green area?
[tex]0.5-0.1255=0.3745[/tex]Therefore, the area to the left of z = -0.32 is 0.3745 or 0.375.
A motorboat travels 392 kilometers in 7 hours going upstream and 384 kilometers in 4 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?rate of the boat in still water ___rate of the current:____
B= speed of the boat in still water
C = speed of the stream
speed upstream = B-C
Speed downstream = B+C
distance = Rate x time
upstream
392 = (B-C) 7
Downstream
384 = (B+C) 4
Solve the system of equations:
392 = 7B-7C (a)
384 = 4B + 4C (b)
Solve (a) for B:
392+7c = 7B
(392+7c) /7 = B
B = 56+c
Replace the value of B on equation (b) and solve for c
384 = 4 (56 +c) + 4c
384 = 224 + 4c +4c
384-224 = 4c+4c
160 = 8c
160/8 = c
20 = c
Replace c on (a)
392= 7B -7 (20)
392 = 7B -140
392+140 = 7B
532= 7b
B = 532/7
B= 76
c= 20
B= 76
10. Sylvie needs $90.50 for a concert ticket. She already has $8 and she can earn the rest by working 7 hours at her job. Fill in the boxes to write an equation that can be solved to find h, Sylvie's hourly earnings.
We know that
• She needs $90.50 in total.
,• She has $8.
,• 7h is the amount she can earn at her job.
Having said that, we can define the following equation
[tex]7h+8=90.50[/tex]Then, we solve for h
[tex]\begin{gathered} 7h=90.50-8 \\ h=\frac{82.5}{7} \\ h=11.79 \end{gathered}[/tex]Sylvie's hourly earnings are $11.79.I’m not sure how to answer this question assistance would be nice
1. We are asked to evaluate 10^3. As ten is to the third power, we know that we have to times it by itself three times.
= 10*10*10
=1000
2. 0.079 * x = 7.9
When looking at 0.079, we can see that the last digit 9 is three places behind the decimal point.
When looking at 7.9, we can see that the nine is now only one place behind the decimal point. The decimal point has therefore been moved two spaces. In order to do this, we can times 0.079 by 100 as one hundred has two zeroes.
Therefore:
0.079*100 = 7.9
This table represents a relationship between x and y, where x is the independent variable. 1 2 3 4 5 y 6 7 00 9 10 Which equation represents the relationship between x and y? O x = y +5 o y = 5x O x= 5y O y = x + 5
We are given a table between two variables x and y.
Recall that the equation of a linear relationship is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex]Let us select two (x, y) pairs from the given table
Let us select (1, 6) and (2, 7)
[tex]\text{where}(x_1,y_1)=(1,6)\text{and}(x_2,y_2)=(2,7)[/tex]Let us substitute these values into the slope formula
[tex]m=\frac{y_2−y_1}{x_2−x_1}=\frac{7-6}{2-1}=\frac{1}{1}=1[/tex]So, the slope is 1 and the equation becomes
[tex]y=x+b[/tex]Now let us find the y-intercept (b)
Let us select any one (x, y) pair from the given table.
Let us select (1, 6) and substitute it into the above equation
[tex]\begin{gathered} y=x+b \\ 6=1+b \\ 6-1=b \\ 5=b \\ b=5 \end{gathered}[/tex]Therefore, the equation is
[tex]y=x+5[/tex]The last option is the correct answer.
1. What is the total area of this figure? How to calculate it?
Given the figure shown in the exercise, you can identify that it is formed by a triangle and a rectangle. Then, the total area of the figure will be the sum of the area of the triangle and the area of the rectangle.
• The formula for calculating the area of a rectangle is:
[tex]A_r=lw[/tex]Where "l" is the length and "w" is the width.
In this case:
[tex]\begin{gathered} l=8ft \\ w=2ft \end{gathered}[/tex]Then, by substituting the values into the formula and evaluating, you get:
[tex]A_r=\left(8ft\right)\left(2ft\right)=16ft^2[/tex]• The formula for calculating the area of a triangle is:
[tex]A_t=\frac{bh}{2}[/tex]Where "b" is the base and "h" is the height of the triangle.
In this case, you can identify that:
[tex]\begin{gathered} b=8ft \\ h=16ft-2ft=14ft \end{gathered}[/tex]See the picture below:
Knowing the base and the height of the triangle, you can substitute values into the formula and evaluate, in order to find its area:
[tex]A_t=\frac{\left(8ft\right)\left(14ft\right)}{2}=\frac{112ft^2}{2}=56ft^2[/tex]Therefore, you can determine that the total area of the figure is:
[tex]\begin{gathered} A_{total}=16ft^2+56ft^2 \\ \\ A_{total}=72ft^2 \end{gathered}[/tex]Hence, the answer is:
[tex]A_{total}=72ft^2[/tex]what is the range of the function f(x) = 3x - 1 when the domain is {-3, -2, -1}?A. {-9, -6, -3}B. {-10, -7, -3}C.{-10, -7 , -4}D.{8,5,2}
what is the range of the function f(x) = 3x - 1 when the domain is {-3, -2, -1}?
A. {-9, -6, -3}
B. {-10, -7, -3}
C.{-10, -7 , -4}
D.{8,5,2}
Find the value of f(x) for the different values of x
so
For x=-3
f(x)=3(-3)-1
f(x)=-10
For x=-2
f(x)=3(-2)-1
f(x)=-7
For x=-1
f(x)=3(-1)-1
f(x)=-4
therefore
teh answer is the option C.{-10, -7 , -4}
Part 2Determine the range for the function given the domain {-2, 0, 2}
y=x^2 + 3
substitute the values of x and solve for y
For =-2
y=(-2)^2+3
y=4+3=7
For x=0
y=(0)^2+3
y=3
For x=2
y=(2)^2+3
y=7
the range is the set {7,3,7}
You are shopping for a car. You are looking at a model that has 5 different exterior color options, 4 different interior color options, 2 different wheel choices and 3 choices for a sound system. how many different unique cars could be formed?
ANSWER
120
EXPLANATION
The car model has the following options:
• 5 exterior colors
,• 4 interior colors
,• 2 wheel choices
,• 3 sound system choices
Each choice is independent of the other - i.e. the interior color does not depend on the exterior color or the wheel choice. So,
[tex]5\cdot4\cdot2\cdot3=120[/tex]Hence, 120 unique cars can be formed.
Two cylinder shaped cans are placed next to each other.Can 1- Radius =1Can 2- Radius =3What is the relationship between the volume of the large can and volume of the small can.A. The volume of the large can is 3x the volume of the small canB. The volume of the large can is 6x the volume of the small canC. The volume of the large can is 9x the volume of the small canD. The volume of the large can is 18x the volume of the small can(I think it's A)
so the volume of the large can is 9x the volume of the small can ( option C)
r - 20 = 19A. Add 20 to both sides B. Subtract 20 from both sides C. Add 19 to both sides D. Subtract 19 from both sides
The answer is A. we add 20 to both sides to isolate the variable r.
Slove the equation-4x + 1 = 21
We have the following:
[tex]-4x+1=21[/tex]solving for x:
[tex]\begin{gathered} -4x+1-1=21-1 \\ -4x=20 \\ x=\frac{20}{-4} \\ x=-5 \end{gathered}[/tex]The answer is -5
Solve the one step equations by using inverse operations. Questions 20-22
The following is a list of 5 measurements.5, 17, 10, 13, 19Send data to calculatorSuppose that these 5 measurements are respectively labeled X2, X2, ..., Xs. Compute the following.5Σ (4)i=1
We will have the following:
[tex]\sum ^5_{i=1}(x_i)^2=(5)^2+(17)^2+(10)^2+(13)^2+(19)^2\Rightarrow\sum ^5_{i=1}(x_i)=944[/tex]So, the given sum is equal to 944.
what's the 1cm in reality.....?
1 centimeter:
A centimeter is metric unit of length, which is used to measure the length of an object.
Example: A pen is 2 cm . Here, the length of pen is measured in the centimeter.l
Each 1 cm is worth 0.25 km. and when we have 10 milimeters we can