Answer:
a
Step-by-step explanation:
Mike's grandmother opened a savings account in Mike's name and deposited some money into the account. The account pays an annual simple interest rate of 9%. After 8 years, the interest earned on the account was $1,440. How much money did Mike's grandmother deposit in the account?
Prove the divisibility of the following numbers:
51^7-51^6 by 25
To prove the divisibility lets expand each number first to get the complete picture of the problem
51^7 = 8.974106779 . 10^11
51^6 = 1.75962878 . 10^10
(51^7 - 51^6) = 8.974106779 . 10^11 - 1.75962878 . 10^10
= 8.798143901. 10^11
[tex]\frac{8.798143901. 10^11}{25}[/tex]
= 3.51925756. 10^10
That is the answer expressed in scientific notation
= 35192575600
Which means the divisibility is proven
Step-by-step explanation:
[tex]51^7-51^6=51^{6+1}-51^6\\\\\text{use}\ a^n\cdot a^m=a^{n+m}\\\\=51^6\cdot51^1-51^6\cdot1\\\\\text{use the distributive property}\ a(b-c)=ab-ac\\\\=51^6\cdot(51-1)=51^6\cdot50=51^6\cdot(2\cdot25)=25\cdot(51^6\cdot2)[/tex]
[tex]\text{One of the factors of the product is the number 25.}\\\\\bold{CONCLUSION:}\\\\\text{The whole product is divisible by 25.}[/tex]
[tex]\text{Therefore}\ 51^7-51^6\ \text{is divisible by 25.}[/tex]
I need desperate help
Graph each figure and classify it. Then find the area.
Answer:
This is a Trapezoid! It has 22 [tex]units{2}[/tex]
Can someone help plz? Thx
45 POINTS PLEASE HELP IT IS DUE TONIGHT THANK U I WILL MARK U BRAINLIEST
Multiply r2+7r+10/3 by 3r-30/ r2-5r-50
I'll give brainliest if you show your work. Plz answer quickly in less than 45 minutes.
Which two points should the line of best fit go through to best represent the data in the scatterplot?
(1, 16) and (2, 15)
(1, 16) and (6, 1)
(2, 15) and (4, 9)
(5, 8) and (6, 1)
Answer:
2,15 and 4,9
Step-by-step explanation:
this is because these two points are in between the other two sets of points.
Bryce spent $ 5.26 on some apples priced at $ 0.64 each and some pears priced at $ 0.45 each. At another store I could have bought the same number of apples at $ 0.32 each and the same number of pears at $ 0.39 each, for a total cost of $ 3.62. How many apples and how many pears did Bryce buy?
a. Write equations to represent Bryce's expenditures at each store. Second store:
First store:
b. Solve the system Number of pears:
Number of apples:
Number of pears:
Some students were surveyed about how much time they spent playing video games last week and their overal test average.
Find the equation of the least-squares line.
Interpret the meaning of the slope.
Interpret the meaning of the y-intercept mathematically.
State the correlation coefficient. Describe any possible correlation for the data set. Use the correlation coefficient to support your answer.
Use the equation of the least-squares line from part a to predict the test average for someone who plays 5 hours of video games a week.
Owen used these steps to solve the equation 4x+7=1+2(2x+3) . Which choice describes the meaning of his result, 7=7 ?
a.The result is not correct because Step 2 has an error.
b.The solution is x=7.
c.No values of x make the equation true.
d.All values of x make the equation true.
The choice that describes the meaning of the result is,
all values of x make the equation true.
The correct option is d.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Owen used these steps to solve the equation,
4x+7 = 1+2(2x+3).
Simplifying,
4x + 7 = 1 + 4x + 6
4x + 7 = 4x + 6 + 1
4x + 7 = 4x + 7
Subtract 4x to both sides,
7 = 7.
That means, the equation has infinitely many solutions.
Therefore, all values of x make the equation true.
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Find the area of each figure. Round to the nearest tenth if necessary
A store gets a bucket of eggs for $16.20 and sells a dozen eggs for $3.50. If there are 450 eggs in the bucket, by what percent has the store increased the price per dozen eggs?
The store has increased the price per dozen eggs by approximately 64.57%.
Explanation:To calculate the percent increase in price per dozen eggs, we can compare the old price per dozen eggs to the new price per dozen eggs. The original price per dozen eggs is $3.50, and the new price per dozen eggs can be calculated by dividing the total cost of the bucket of eggs by the number of dozens it contains. Since there are 450 eggs in the bucket and a dozen is equal to 12 eggs, the new price per dozen eggs is $16.20 / (450 / 12) = $5.76.
To find the percent increase, we can use the formula:
Percent increase = (new price - original price) / original price * 100%
Substituting the values into the formula, we have:
Percent increase = ($5.76 - $3.50) / $3.50 * 100%
Percent increase = $2.26 / $3.50 * 100%
Percent increase ≈ 64.57%
The store increased the price per dozen eggs by approximately 710.19%.
To determine by what percent the store has increased the price per dozen eggs, we first need to calculate the original price per dozen and then compare it to the selling price per dozen.
Step-by-Step Calculation:
1. Calculate the original price per egg:
[tex]\[ \text{Total cost of 450 eggs} = \$16.20 \][/tex]
[tex]\[ \text{Cost per egg} = \frac{\$16.20}{450} = \$0.036 \text{ per egg} \][/tex]
2. Convert the cost per egg to the cost per dozen:
[tex]\[ \text{Cost per dozen} = \$0.036 \times 12 = \$0.432 \][/tex]
3. Given selling price per dozen:
[tex]\[ \text{Selling price per dozen} = \$3.50 \][/tex]
4. Calculate the price increase per dozen:
[tex]\[ \text{Price increase per dozen} = \$3.50 - \$0.432 = \$3.068 \][/tex]
5. Calculate the percent increase:
[tex]\[ \text{Percent increase} = \left( \frac{\$3.068}{\$0.432} \right) \times 100 = 710.19\% \][/tex]
- The store has increased the price per dozen eggs by approximately 710.19%.
Can someone help with this question. Please show your work, thanks!
A baseball player got 10 hits in 39 times at bat. What percent of his times at bat did he get a hit? (Round to the nearest percent.)
Answer:
26%
because I did the Math so don't ask OKAY!
Help please? I don't understand..!
Light travels at a speed of about 3.0x10^8 meters per second. How far does light travel in 4,500 seconds You Would Get __ E __
light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.
To find out how far light travels in 4,500 seconds, we can use the formula:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Given that the speed of light is approximately [tex]\( 3.0 \times 10^8 \)[/tex] meters per second and the time is 4,500 seconds, we can plug these values into the formula:
[tex]\[ \text{Distance} = 3.0 \times 10^8 \text{ m/s} \times 4,500 \text{ s} \][/tex]
Calculating this gives us:
[tex]\[ \text{Distance} = 1.35 \times 10^{12} \text{ meters} \][/tex]
So, light would travel approximately [tex]\( 1.35 \times 10^{12} \)[/tex] meters in 4,500 seconds.
Simplify the answer
1 - 5/6?
miguel ran 1 3/10 miles on monday. on friday miguel ran 3 times as far as he did on monday. how much farther did miguel run in friday than he did on monday?
Final answer:
Miguel ran different distances on Monday and Friday. We calculate how much farther he ran on Friday than on Monday to find the difference in distance.
Explanation:
Miguel ran 1 3/10 miles on Monday. On Friday, Miguel ran 3 times as far as he did on Monday. To find out how much farther Miguel ran on Friday than on Monday, we first calculate how far he ran on Friday, which is 1 3/10 miles x 3 = 3 9/10 miles. The difference in distance is 3 9/10 - 1 3/10 = 2 6/10 miles.
The perimeter of a sand volleyball court is 52 meters. The area is 153 square meters. What are the dimensions of the volleyball court?
To find the dimensions of the volleyball court, set up a system of equations using the perimeter and area formulas. Solve the equations to find the possible dimensions of the court.
Explanation:To find the dimensions of the volleyball court, we can set up a system of equations using the given information. Let's represent the length of the court as 'l' and the width as 'w'. We know that the perimeter of a rectangle is given by the formula 2l + 2w, so we can set up the equation 2l + 2w = 52. Additionally, we know that the area of a rectangle is given by the formula lw, so we can set up the equation lw = 153.
Using these equations, we can solve for the dimensions of the volleyball court. Let's solve the first equation for l: 2l = 52 - 2w. Dividing both sides by 2 gives us l = 26 - w. Now we can substitute this value of l into the second equation: (26 - w)w = 153. Expanding this equation gives us w^2 - 26w + 153 = 0. We can solve this quadratic equation using factoring, the quadratic formula, or by graphing. After solving for w, we can substitute this value back into the equation l = 26 - w to find the length of the court.
After solving the quadratic equation, we find two possible values for the width: w = 9 and w = 17. Plugging each value into the equation l = 26 - w, we find the corresponding lengths: l = 17 and l = 9. Therefore, the possible dimensions of the volleyball court are 17m by 9m or 9m by 17m.
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Plot the x- and y-intercepts to graph the equation. y=13x−1 .
PLEASE plot it on a graph PLEASE and i will get you brainly and 15 points
Answer:
Given the equation: [tex]y = \frac{1}{3}x -1[/tex] .....[1]
To find the intercepts:
x-intercepts states that the graph cross the x-axis.
Substitute the value of y = 0 in [1] to solve for x;
[tex]0 = \frac{1}{3}x-1[/tex]
Add 1 to both sides we get;
[tex]1 = \frac{1}{3}x[/tex]
Multiply both sides by 3 we get;
[tex]3 = x[/tex]
x-intercepts = (3, 0)
y-intercepts states that the graph cross the y-axis
Substitute the value x = 0 in [1] to solve for y;
[tex]y = \frac{1}{3}(0) -1[/tex]
Simplify:
y = -1
y-intercept = (0, -1)
Now, using these x- and y--intercepts points to graph the given equation [tex]y = \frac{1}{3}x -1[/tex] as shown below.
What is the surface area of this right rectangular prism? Enter your answer in the box.
Answer: [tex]76\ m^2[/tex]
Step-by-step explanation:
The surface area of a rectangular prism is given by :-
[tex]\text{Surface area}=2(lw+wh+hl)\\\\\Rightarrow\ \text{Surface area}=2(4\cdot5+2\cdot5+2\cdot4)\\\\\Rightarrow\ \text{Surface area}=2(20+10+8)\\\\\Rightarrow\ \text{Surface area}=2(38)\\\\\Rightarrow\ \text{Surface area}=76\ m^2[/tex]
Hence, he surface area of this right rectangular prism= [tex]76\ m^2[/tex]
Which property changes when a figure is translated
A function has a constant tripling time. What type of function does this represent ?
A. Expontential decay
B. Decreasing linear
C. Increasing linear
D. Exponential growth
Answer: This represented a exponential growth function.
Step-by-step explanation:
Exponential growth is demonstrated when the rate of change of the value of any mathematical function[the change per unit of time] is proportional to the function's present value, resulting in its value at any time being an exponential function of time or becomes a function in which the time value is the exponent.
Given : A function has a constant tripling time. So it is highly increasing (exponentially) with the time i.e. the function is exponential function.
Answer: Hello mate!
A constant tripling time means that there is a time T, a quantity triples when t = T, then triples again when t = 2T, and again when t = 3T.
Then if A is the initual cuantity; we have a function of the form
f(t) = A*3^(t/T)
and you can see that:
f(0) = A
f(T) = A*3
f(2T) = A*3^2 = (A*3)*3
and so on:
This function describes an exponential growth (because f(t) increases exponentialy over time)
Please give answer and explain please.
The high soccer team can have no more than 26 players. Write and solve an inequality to determine how many more players can make the team if the coach has already chosen 17 players
The table given are for the linear functions f(x) and g(x) what is the input value for which f(x) = g(x) is true ?
x=
The functions f(x) and g(x) will be equal at x = -1 the input value will be -1.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have:
Two function f(x) and g(x) shown in the table.
From the table:
At x = -1
f(-1) = 3
At x = -1
g(-1) = 3
f(-1) = g(-1)
or
f(x) = g(x) at x = -1
Thus, the functions f(x) and g(x) will be equal at x = -1 the input value will be -1.
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the measure of an angle is 34 degrees what is the measure of its supplement
The measure of the supplement angle is 146 degrees.
What are supplementary angles?The supplementary angles is defined as when pair of angles addition to 180° then they are called as supplementary angles. There are two types of supplementary angles.
What are Adjacent angles?Adjacent angles is the type of supplementary angles. Adjacent angles have a common side and vertex, for example a corner point. Their points do not overlap in any way. In other terms, adjacent angles is pair of two angles next to each other
Given that the measure of an angle is 34 degrees
Let x = the measure of the supplement angle.
Two angles whose sum is 180 degrees are supplementary.
∴ x + 34 = 180
Then, (180 -34 ) is the supplement of that angle.
The measure of the supplement angle = 146 degrees
Hence, the measure of the supplement angle is 146 degrees.
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how do you find the equation of a linear model when given the graph but not the equation
We want to see how to find a linear equation by only looking at the line graph.
First, a general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Then the line is something like:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + b[/tex]
To get the value of b, we use the fact that if the function passes through (x₁, y₁), it means that when x = x₁ we also must have y = y₁, replacing that in the equation we get:
[tex]y_1 = (\frac{y_2 - y_1}{x_2 - x_1})*x_1 + b\\\\y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1 = b[/tex]
Then the linear equation is:
[tex]y = (\frac{y_2 - y_1}{x_2 - x_1})*x + y_1 - (\frac{y_2 - y_1}{x_2 - x_1})*x_1[/tex]
So what we need to do is just look at the graph and find two points, then you can use the above guide to find the linear equation.
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Last year the attendance at the homecoming football game was 300.This year 360 people attended.What was the percent increase from last year to this year