A scatter plot is made with the data shown below: Number of Bakers at a Cake Shop 5 6 7 8 9 10 11 12 13 Number of Cakes Baked 7 7 8 8 9 11 13 14 14 What type of association will the scatter plot for these data represent between the number of bakers at the cake shop and the number of cakes baked? No association Positive linear association Negative linear association Positive nonlinear association
Answer:
positive linear association
hope this helps
The equation A=p(1+r)^t can be used to calculate compound interest on a savings account. A = future balance, p = current balance, r = rate of interest, and t = time in years. If you deposit $2,000 at 10% each year, how much money will be in your account in 10 years
Using the formula for compound interest, if you deposit $2,000 at 10% each year, the future balance in your account after 10 years would be approximately $5,187.12. This is due to the effect of compounding where the interest is calculated on both the principal and the accumulated interest.
Explanation:The subject of this question is compound interest which is a Mathematics topic typically covered in High School. The formula A=p(1+r)^t is used to calculate the future balance in your savings account considering compound interest. Here, 'A' represents the future balance, 'p' is the current principle or balance, 'r' is the rate of interest, and 't' is time in years.
To answer your specific question: If you deposit $2,000 at a 10% rate each year, how much money will be in your account in 10 years? Let's plug the numbers into the formula. In this case, p=$2000, r=0.10 (as 10% equals 0.10 in decimal), and t=10 years.
So, A = 2000*(1 + 0.10)^10. Solving this, the future balance in your account after 10 years would be approximately $5,187.12. This is significantly more than simple interest ($100 × 0.05 × 3 = $15 in your example) due to the effect of compounding, as the interest is calculated on the principal plus the accumulated interest.
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Which of the following represents the zeros of f(x) = 4x3 − 13x2 − 37x + 10? 5, −2, −1 over 4 5, −2, 1 over 4 5, 2, −1 over 4 5, 2, 1 over 4
Answer:
The three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.
Step-by-step explanation:
The given polynomial is,
[tex]f(x)=4x^3-13x^2-37x+10[/tex]
Use hit and trial method, Put x=-2
[tex]f(x)=4(-2)^3-13(-2)^2-37(-2)+10=0[/tex]
Since the value of function is 0 at x=-2 therefore (x+2) is a factor of the given polynomial.
Divide the given polynomial by using synthetic division or long division.
[tex]f(x)=(x+2)(4x^2-21x+5)[/tex]
Use grouping method to find the factors,
[tex]f(x)=(x+2)(4x^2-20x-1x+5)[/tex]
[tex]f(x)=(x+2)(4x(x-5)-(x-5))[/tex]
[tex]f(x)=(x+2)(x-5)(4x-1)[/tex]
Equate each factor equal to 0.
[tex]x=-2,5,\frac{1}{4}[/tex]
Therefore, the three zeros are 5 , -2 and [tex]\frac{1}{4}[/tex]. The second option is correct.
What is the distance from (−3, 1) to (−1, 5)? Round your answer to the nearest hundredth.
A.3.60
B. 4.12
C.4.47
D.5.66
pls
Answer:
c 4.47
Step-by-step explanation:
got it right on my test
The distance from (−3, 1) to (−1, 5) is 4.47
What is slope of line?
Slope of line is defined as the angle of line.
The distance between two points is found by
[tex]d = \sqrt{( (x_2-x_1)^2 + (y_2-y_1)^2)}[/tex]
[tex]d = \sqrt{ ( (-1--3)^2 + (5-1)^2)}[/tex]
[tex]d=\sqrt{( (2)^2 + (4)^2)}[/tex]
[tex]d=\sqrt{(4+16)}[/tex]
[tex]d=\sqrt{(20)}[/tex]
d = 4.472135955
Rounding to the nearest hundredth
d = 4.47
Hence, the distance from (−3, 1) to (−1, 5) is 4.47
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2/9 divided by 5/12?
Please simplify in its simplest form
2/9 divided by 5/12 simplifies to 2/15
Here we have to divide,
2/9 divided by 5/12
To divide fractions,
We have to flip the second fraction and multiply it by the first fraction. This gives us,
⇒ (2/9) ÷ (5/12) = (2/9) x (12/5)
We can simplify this expression by canceling out any common factors between the numerators and denominators.
In this case,
2 and 12 have a common factor of 2, while 9 and 5 don't have any common factors. This gives us,
⇒ (2/9) x (12/5) = 24/45
To express this fraction in its simplest form,
we can divide both the numerator and denominator by their greatest common factor, which in this case is 3.
This gives us,
6/45 = (24 ÷ 3) / (45 ÷ 3)
= 8/15
Therefore, 2/9 divided by 5/12 simplifies to 8/15.
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Which of the following equations has a graph that crosses the y-axis at a point lower than y=2x^2-1
A.y=-3x^2+1
B.y=3x^2-3
C.y=-3^2-1
D.y=-3^2+3
A particular car gets fuel mileage of 36 mpg in the city and 12% more on the highway.
What is the car's fuel mileage on the highway?
The car's fuel mileage on the highway is 40.32 mpg, which is 12% more than the 36 mpg it gets in the city.
To determine the car's fuel mileage on the highway, given that it is 12% more than the fuel mileage in the city, we start with the given city mileage of 36 miles per gallon (mpg). We calculate the additional mileage gained on the highway by taking 12% of 36 mpg, which is 0.12 × 36 mpg = 4.32 mpg. Adding this to the city mileage gives the highway mileage:
36 mpg + 4.32 mpg = 40.32 mpg on the highway.
I NEED THIS DONE, PLEASE HELP...
Fill in the blank:
To prove that the medians of an isosceles triangle meet at a point, show that the ____ of a side lies on the line containing the opposite _____ and the point where the other two ____ intersect
If three lines meet at a single point, we say that the lines are concurrent.
Note that median is a line joining one vertex of a triangle with the midpoint of its opposite side.
Draw two medians for the given isosceles triangle.
Now, join the point of intersection of these medians and the third vertex.
If we prove the midpoint of the opposite side lies on this line, then it will be proved that the medians of the given isosceles triangle meet at a point.
Hence, here is the correct statement with blanks filled.
The midpoint of a side lies on the line containing the opposite vertex and the point where the other two medians intersect.
Between what pair of numbers is the product of 289 and 7?
Your running speed is 8.5 miles per hour. A greyhound dog's speed is about 4.5 times faster than yours. What is the dog's speed?
Is it possible to represent the number 203 as a sum of several whole numbers such that their product is also equal to 203?
answer both questions if you cant see all the answers its fine all u need is the question
You want to buy an item that costs $100. Which is the most cost-effective choice for buying the item?
Compare prices, consider discounts, and watch for additional costs like shipping. Choose the option with the lowest total expense for buying the $100 item.
To determine the most cost-effective choice for buying the $100 item, you should consider any available discounts, promotions, or deals offered by different sellers or platforms. Here are a few strategies you could consider:
1. **Comparison Shopping**: Check multiple retailers or online platforms to see if the item is available at a lower price elsewhere. Websites and apps dedicated to comparison shopping can help streamline this process.
2. **Discounts and Coupons**: Look for any available discounts or coupons that you can apply to your purchase. Many retailers offer promotional codes or special deals that can help reduce the cost of the item.
3. **Cashback and Rewards**: Some credit cards or loyalty programs offer cashback or rewards points for purchases. If you have a card or program like this, see if you can earn rewards or cashback by buying the item through a specific retailer.
4. **Timing**: Consider timing your purchase to coincide with sales events or promotions, such as Black Friday, Cyber Monday, or seasonal sales. Buying during these periods can often result in significant savings.
5. **Shipping and Handling Costs**: Be mindful of any additional costs associated with shipping and handling. Sometimes, even if the base price of the item seems lower from one seller, the shipping costs may make the overall purchase more expensive.
By comparing prices, looking for discounts, and considering additional costs, you can find the most cost-effective option for purchasing the $100 item.
Complete Question:
Which of these is the most cost effective choice for buying the item using a paid membership card to buy it at a 10 percent discount buying it on line at a 10 percent discount without sales tax?
find k if the lines 3x-5y=9 and 2x+ky=11 are a) parallel and b) perpendicular
a) To find k for parallel lines, equate slopes to get k = -10/3. b) For perpendicular lines, use negative reciprocal slopes to find k = 3/10.
To determine the conditions for parallelism and perpendicularity, we need the slope of each line. The slope-intercept form of a line is y = mx + b where m is the slope.
To find the slope of the first line, we rearrange 3x-5y=9 to the form of y = mx + b, resulting in y = (3/5)x - (9/5). Therefore, the slope is 3/5. For the second line, rearranging 2x+ky=11 gives us y = (-2/k)x + (11/k). The slope of the second line is -2/k.
For the lines to be parallel, their slopes must be equal, so 3/5 = -2/k. Solving for k, we get k = -10/3. For the lines to be perpendicular, the product of their slopes must be -1 (since perpendicular lines have negative reciprocal slopes). This gives us (3/5)(-2/k) = -1, and solving for k yields k = 3/10.
In your own words explain the place value relationship when the same two digits are next to each other in a multi digit number
In a place value relationships. The relationship between 2
the same digit place next to each other is the value of the number to left is
10 times bigger than to the value to the left and from the decimal point to the
right is 10 times smaller of value than the digit in their right.
Let say for example:
1111
1 thousands, 1 hundreds, 1 tens, and 1 ones.
Let’s start from 1 = 1 x 10 = 10
That would be 10 X 10 = 100
then 100 X 10 = 1000
Notice that their value increase base on its place value if
we multiply the given number by 10.
Another one is
912.98 in where 9 is hundreds, 1 is tens, 2 is ones and after
the decimal points, in where 9 is tenths and 8 is hundredths.
Notice each place value next to each other. Each value is ten
times in difference.
What is the next value 1I2L3F4
(sum of 50 different whole numbers, each less than 51)-(sum of 45 different whole numbers, each less than 51)is at most
A:10
B:15
C:240
D:285
the legs of a right triangle are 75 and 100. what is the length of the hypotenuse?
A: 5 square root 5
B: 250
C:125
D: 625
right triangle us pythagorean theorem
a^2 + b^2 = c^2
75^2 + 100^2 = C^2
5625 +10000 = c^2
15625 =c^2
c=Sqrt(15625) = 125
hypotenuse = 125
answer is C
The profit on the sale of a small bag of popcorn is $1, while the profit on the sale of a medium bag of popcorn is $2. The Glee Club expects to sell fewer than 100 total bags of popcorn, but they hope to make more than $100 in profit. The system that represents this is s+m<100 and s+2m>100. The graph of the boundary lines is shown below. Which regions should be shaded (to form the solution)?
A triangle can be formed with side lengths 5, 7 and 10. True or False
The width of a vegetable garden is 3 times it's length.If the length of the garden is 4 1/2 feet,what is the width in simplest form?
Ten times the sum of half a number and 6 is 8
3/5b-8=4, step by step plz
The profit function for a new product is given by p(x) = -4x^2+28x-40, where x is the number sold in thousands. How many items must be sold for the company to break even?
Final answer:
The company must sell either 2,000 or 5,000 items to break even, as determined by setting the profit function to zero and factoring the resulting quadratic equation.
Explanation:
To determine how many items must be sold for the company to break even, we need to set the profit function p(x) equal to zero and solve for x. In this case, the profit function is given by p(x) = -4x^2 + 28x - 40. Setting this to zero, we have:
-4x^2 + 28x - 40 = 0
Now, we need to solve this quadratic equation for x. To do this, we can factor the equation, use the quadratic formula, or complete the square. Since the coefficients are manageable, we'll try to factor first:
-4(x^2 - 7x + 10) = 0
Let's look for two numbers that multiply to 10 and add up to 7, which are 5 and 2. We can now factor further:
-4(x - 5)(x - 2) = 0
From the factored form, we get two potential solutions for x when the profit is zero:
x = 5
x = 2
Since x represents the number of items sold in thousands, the company must sell either 2,000 or 5,000 items to break even.
3x (2•5) + 45= n
What is n???
Mrs. Ming invested an amount of money in two accounts for one year. She invested some at 8% interest and the rest at 6% interest. Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest. How much had Mrs. Ming invested in the account paying 6%? $117 $680 $760 $820
Answer:
The correct option is B) $680.
Step-by-step explanation:
Consider the provided information.
Her total amount invested was $1,500. At the end of the year, she had earned $106.40 in interest.
Let she invested x amount with 8% interest rate.
Total amount she invested was $1,500, thus the amount she invested with 6% interest rate was 1500-x.
Total interest she earn was $106.40
Write this information into mathematical form.
[tex]x\times \frac{8}{100}+\frac{6}{100}(1500-x)=106.40[/tex]
[tex]x\times 0.08+0.06(1500-x)=106.40[/tex]
[tex]0.08x+90-0.06x=106.40[/tex]
[tex]0.08x-0.06x=106.40-90[/tex]
[tex]0.02x=16.4[/tex]
[tex]x=820[/tex]
Hence, she invested $820 with 8% interest rate.
The amount she invested with 6% interest rate was 1500-x.
Substitute the value of x in above.
1500-820=680
Hence, she invested $680 with 6% interest rate.
The correct option is B) $680.
How to write 15,409 in word form
PLEASE HELP I'M BEING TIMED!!!!
if the diameter of a youth softball is 3.5 inches and the diameter of an adult softball is 3.8 inches, what is the approximate difference in their volumes? Use 3.14 for pi . Round to the nearest tenth of a cubic inch.
A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers
Final answer:
The slope for a line passing through two points can be found using the formula m = (y2 - y1) / (x2 - x1). By substituting the given points into the formula, the slope for the line passing through (1, 0.1) and (7, 26.8) is found to be 4.5.
Explanation:
The formula for the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
To find the slope for the given points (1, 0.1) and (7, 26.8), we can substitute the values into the formula:
m = (26.8 - 0.1) / (7 - 1) = 4.5
Therefore, the slope for the line passing through the given points is 4.5.
a. The equation for the line in point-slope form is [tex]\( y + 1 = \frac{5}{6}(x - 2) \).[/tex]
b. The equation in standard form is ( 5x - 6y = 16 ).
Explanation:a. To find the equation of the line in point-slope form, we use the formula [tex]\(y - y_1 = m(x - x_1)\)[/tex], where (m) is the slope and [tex]\((x_1, y_1)\)[/tex] is a point on the line. Given the points (2, -1) and (8, 4), we can calculate the slope (m) as [tex]\(\frac{{y_2 - y_1}}{{x_2 - x_1}}\)[/tex]. Substituting the values, we get:
[tex]\[ m = \frac{{4 - (-1)}}{{8 - 2}} = \frac{5}{6} \][/tex]
Now, using the point-slope form, we substitute the values for (m) and [tex]\((x_1, y_1)\)[/tex]:
[tex]\[ y + 1 = \frac{5}{6}(x - 2) \][/tex]
b. To convert the equation to standard form, we want to eliminate fractions and express it as (Ax + By = C), where (A), (B), and (C) are integers. Multiply both sides of the equation by 6 to clear the fraction:
6(y + 1) = 5(x - 2)
Distribute the terms:
(6y + 6 = 5x - 10)
Bring all terms to one side:
[ 5x - 6y = 16 ]
So, the equation in standard form is (5x - 6y = 16). This form is preferred for certain applications, making it easier to identify coefficients and intercepts.
A mountain climber explored a cliff that is 225 yards high in 5 equal trips. How many yards was one trip?