Answer:
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
Step-by-step explanation:
Let
x ---> the amount invested in the 8% interest account
41,500-x ----> the amount invested in the 15% interest account
we know that
The amount invested in the 8% interest account multiplied by the interest in decimal form plus the amount invested in the 15% interest account multiplied by the interest in decimal form, must be equal to $5,490
so
The linear equation that represent this problem is
[tex]0.08x+0.15(41,500-x)=5,490[/tex]
solve for x
[tex]0.08x+6,225-0.15x=5,490\\0.15x-0.08x=6,225-5,490\\0.07x=735\\x=\$10,500[/tex]
so
[tex]41,500-x=41,500-10,500=\$31,000[/tex]
therefore
$10,500 in the 8% interest account,
$31,000 in the 15% interest account
You volunteer at an animal shelter on the weekends and today is adoption day! At the beginning of the event, you start with 44
44
cats/kittens.
x
number of cats/kittens get adopted. But then, at the end of the day, someone drops off twice as many new cats/kittens as were adopted. You now have 50
50
cats/kittens.
How many
cats/kittens were adopted.
6 cats/kittens were adopted.
Step-by-step explanation:
Given,
Number of cats/kittens at the event = 44
Number of cats/kittens adopted = x
Number of cats/kittens returned = Twice returned as adopted = 2x
New total = 50
We will subtract the adopted and add the returned cats/kittens.
Total cats/kittens at event - adopted + returned = New total
[tex]44-x+2x=50\\44+x=50\\x=50-44\\x=6[/tex]
6 cats/kittens were adopted.
Keywords: expression, variables
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answer key for middle school math with pizzazz! book d d-47
Answer:
hola
Step-by-step explanation:
17. WEATHER Heavy rain in Brieanne's town caused the river to rise. The river rose three
inches the first day, and each day after rose twice as much as the previous day. How
much did the river rise in five days?
Answer:
30
Step-by-step explanation:
It states that it rained twice as much in 5 days all you do is multiply the 2 times 3 which is 6 so then u multiply 6 times 5 which is 30.
The river rose a total of 93 inches over five days.
The question asks how much a river rises in five days given a certain pattern of increase. To find the solution, we use a geometric sequence because the river rises by a constant multiple each day. On the first day, the river rises three inches. Since on each subsequent day the river rises by twice the amount it did the previous day, the sequence of increases over five days is: 3 inches, 6 inches, 12 inches, 24 inches, and 48 inches.
The total rise of the river is the sum of these increases:
3 + 6 + 12 + 24 + 48 = 93 inches.
Therefore, the river rose a total of 93 inches over the span of five days.
What’s the slope for Y=8x+2
The student council is planning the school carnival. Each ticket costs $2.50. Explain how to write an equation that represents this scenario. Let x represent the number of tickets sold, and y represent the total amount of money raised.
Answer:
Step-by-step explanation:
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
Answer:
y=2.5x
The total amount of money raised(y) = how many tickets are sold(x) x the price per ticket(2.5)
Hypothetically, if 24 tickets were sold, we could substitute 24 into x...
y=2.5(24)
y=60
Let x represent the number of tickets sold, and y represent the total amount of money raised. Since each ticket is $2.50, the total amount of money raised is equal to $2.50 times the number of tickets. The equation would be y = 2.50x.
The x variable represents the number of tickets sold.
The y variable represents the total amount of money raised from ticket sales.
The equation for the scenario is y = 2.50x.
Someone help me please
Answer:
A because it is increasing
Step-by-step explanation:
Answer:
I would say c
Step-by-step explanation:
you think if you go down a hill what happen is you speed up so you would need to be go down or heading in a negative direction.
In circle L, arc NOP is 90° and the radius is 5 units. Which statement best describes the length of arc NOP?
Answer:
[tex]\frac{1}{4}[/tex] of circumference of the circle
Step-by-step explanation:
We are given that
Arc NOP=Central angle=[tex]\theta=90^{\circ}[/tex]
Radius of circle=5 units
We have to find the statement which describes best the length of arc NOP.
Arc length=[tex]\frac{central\;angle}{360}\times 2\pi r[/tex]
Using the formula
Arc length=[tex]\frac{90}{360}\times circumference\;of\;circle[/tex]
Where Circumference of circle=[tex]2\pi r[/tex]
Arc length NOP=[tex]\frac{1}{4}[/tex]circumference of circle
Hence, the arc length NOP=[tex]\frac{1}{4}[/tex] of circumference of the circle
Answer:
1/4 the circumference of circle L
Step-by-step explanation:
100 increased by 3.1%
Answer:
103,1
Step-by-step explanation:
Use this formula: 100*(1+3.1%)
x + 6y = -7
2x + 12y = -14
ALL OF THESE WILL BE SOLVE FOR X AND Y!!!
Problem 1 Solve For x: x=−6y−7
Show work: Add -6y to both sides.
x+6y+−6y=−7+−6y
x=−6y−7
Problem 1 Solve For y: y = -1/6x + -7/6
Show work: Add -x to both sides.
x+6y+−x=−7+−x
6y=−x−7
Step 2: Divide both sides by 6.
6y/6 = -x -7/6
Problem 2 Solve For x: x=−6y−7
Show work: Add -12y to both sides.
2x+12y+−12y=−14+−12y
2x=−12y−14
Step 2: Divide both sides by 2.
2x/2 = -12y - 14/2
Problem 2 Sovle For y: y=-1/6x + -7/6
Show work: Add -2x to both sides.
2x+12y+−2x=−14+−2x
12y=−2x−14
Step 2: Divide both sides by 12.
12y/12 = -2x-14/12
write an equation in slope - intercept form, and then find the slope and y- intercept 3x-y=14
Answer:
slope-intercept form: y = 3x - 14
slope: 3
y-intercept: -14
Step-by-step explanation:
To find the equation in slope-intercept form, isolate the "y" variable by moving everything to the other side. Slope-intercept form looks like y = mx + b.
"x" and "y" mean points that are on the line.
"m" is the slope.
"b" is the y-intercept.
Rearrange the equation to isolate "y"
3x - y = 14
3x - 3x - y = 14 - 3x Subtract 3x from both sides
-y = 14 - 3x Multiply both sides by -1.
y = -14 + 3x Put "3x" in front of "-14" because it has the 'x'
y = 3x - 14 Looks like y = mx + b
State the "m" and "b".
m = 3 (Slope of the line)
b = -14 (y-intercept of the line)
Therefore the equation of the line in slope-intercept form is y = 3x - 14. The slope is 3 and the y-intercept is -14.
how do you add and subtract
Homework answers plz
Answer: 10.5
Step-by-step explanation:
Hello the answer is 10.5 you just have to multiply 3 1/2 times 3 and there's your answer
Have a great day hope this helps!:):):
Answer:
10 1/2
Step-by-step explanation:
convert 3 1/2 into an improper fraction
3 1/2 = 7/2
if the flour is tripled that means
3 1/2 x 3
= 7/2 x 3
= (7x3) / 2
= 21/2 (convert to mixed fraction, by long division)
= 10 1/2
A frame around a rectangular family portrait has a perimeter of 150 inches. The length is ten more than four times the width. Find the length and width of the frame.
Answer: The length is 62 inches and the width is 13 inches
Step-by-step explanation: The perimeter of the rectangular portrait has been given as 150 inches. We also know that the perimeter of a rectangle is given as
Perimeter= 2(L + W)
However we don't have the measurements for the length and width. What we do have are descriptions of both. The length is given as W, while the length is ten more than four times the width. That is, the length equals
10 + 4W
Therefore we have the length and the width as
L = 4W + 10 and
W = W
If the perimeter is 150, and
Perimeter = 2(L + W) then,
150 = 2(4W + 10 + W)
150 = 2(5W + 10)
150 = 10W + 20
Subtract 20 from both sides of the equation
130 = 10W
Divide both sides of the equation by 10
13 = W
With that in mind we can now calculate the length as
L = 4W + 10
Substitute for the value of W
L = 4(13) + 10
L = 52 + 10
L = 62
Therefore, the length is 62 inches and the width is 13 inches
Answer:
Length = 62 inches, Width = 13 inches
Step-by-step explanation:
Let L represent the length of the frame, W, the width and P, the perimeter
Perimeter of a rectangle, P = 2 (L + W) .....eq 1
Also, P = 150 inches
and
L = 10 + 4W .....eq 2
Slotting in the respective values of P and L in eq 1
150 = 2 {(10 + 4W) + W}
Expanding the bracket
150 + 2 (10 + 5W)
150 = 20 + 10W
Subtracting 20 from both sides of the equation
150 - 20 = 20 - 20 + 10W
130 = 10W
Dividing both sides by the coefficient of W which is 10
13 = W
Therefore, W = 13 inches
Slotting in the value of W in eq 2
L = 10 + 4 (13)
L = 10 + 52
L = 62 inches
Lets ensure that the values of L and W are correct
P = 2 (L + W)
150 = 2 (13 + 62)
150 = 2(75)
150 = 150
Hence, L = 62 inches, W = 13 inches
what is 6(5−8v)+12=−54
Answer:
v = 2
Step-by-step explanation:
What is the slope of (0,1) and (5,4)
Answer:
3/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-1)/(5-0)
m=3/5
Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles, Find the probability of selecting one green marble from bag A and one black marble from bag B.
Answer:
3/20
Step-by-step explanation:
Prob. (For green (Bag A)) = 3/12
Prob. (For Black (Bag B)) = 9/15
3/12 x 9/15 = 3/20
The probability of selecting one green marble from bag A and one black marble from bag B is 0.15
There are 3 green marbles in bag A out of a total of 12 marbles (i.e. 3 green and 9 red).
So, the probability of selecting a green marble from bag A is:
[tex]Pr = \frac 3{12}[/tex]
There are 9 black marbles in bag B out of a total of 15 marbles (i.e. 9 black and 6 orange).
So, the probability of selecting a black marble from bag B is:
[tex]Pr = \frac 9{15}[/tex]
The required probability is then calculated as:
[tex]P = \frac 3{12} * \frac 9{15}[/tex]
Multiply
[tex]P = 0.15[/tex]
Hence, the probability of selecting one green marble from bag A and one black marble from bag B is 0.15
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GL Stats: lviixea conrldence Intervals Practice
On each problem, verify that the conditions for a confidence interval are met!
(1) Suppose the height of senior girls at Anytown High School is known to be normally distributed. A sample of
leights in inches of 23 randomly selected senior girls were: 63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60,
66, 67, 68, 66, 70, 79, 76, 75, 65. Construct and interpret a 99% confidence interval for the true mean height
Answer:
99% Confidence interval: (63.65,69.65
Step-by-step explanation:
We are given the following data:
63, 68, 60, 59, 68, 65, 67, 64, 69, 69, 61, 67, 61, 60, 66, 67, 68, 66, 70, 79, 76, 75, 65
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{1533}{23} = 66.65[/tex]
Sum of squares of differences = 575.217
[tex]S.D = \sqrt{\dfrac{575.217}{22}} = 5.11[/tex]
99% Confidence interval:
[tex]\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]t_{critical}\text{ at degree of freedom 22 and}~\alpha_{0.01} = \pm 2.818[/tex]
[tex]66.65 \pm 2.818(\dfrac{5.11}{\sqrt{23}} ) = 66.65 \pm 3.002 = (63.65,69.65)[/tex]
What is the area of a triangle with A = 15°, B= 113', and b = 7?
a. 3.8 units
c. 5.4 units
b. 4.2 units
d. 4.4 units
Answer:
The answer is C, 5.4 units
Step-by-step explanation:
An Investment of $2,000 is earning interest at the rate of 6.2% compounded quarterly over 5 years. Approximately how much
interest is earned on the investment?
Answer: $720.37
Step-by-step explanation:
interest = 2000(1.0155)^20 - 2000
= 720.37
Hope this helps!!! Good luck!!! :)
Which expression is equivalent to (x3 · x2)5? x10
Step-by-step explanation:
The given expression is
[tex]x^3.x^2[/tex]
To write the given expression is equivalent = ?
The given expression is
[tex]x^3.x^2[/tex]
We know that,
The exponential identity,
[tex]a^{m}.a^{n}=a^{m+n}[/tex]
= [tex]x^{3+2}[/tex]
= [tex]x^{5}[/tex]
∴ The given expression is equivalent = [tex]x^{5}[/tex]
Thus, the given expression is equivalent to [tex]x^{5}[/tex].
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Answer:
The answer to (x3*x2)5 is x25
Step-by-step explanation:
4. Which of the following points are solutions to the system of inequalities 2x - 3y > 9 and -x -
4y > 8?
• (-1,-3)
(1,3)
(-1,3)
(1,-3)
Answer:
(1, -3)
Step-by-step explanation:
Suppose Ellie starts making a lamb stew using a 6.5-quart pot. She decides to make a bigger stew. She pours everything into a pot that is 40 percent bigger. How big is the bigger pot?
Answer:
The bigger pot is a 9.1-quart pot
Step-by-step explanation:
Initial pot size = 6.5-quart
New pot is 40% bigger than the initial pot size
Bigger pot size = 6.5-quart + (0.4 × 6.5-quart) = 6.5-quart + 2.6-quart = 9.1-quart
Give each trig ratio as a fraction in simplest form.
1 point
Sin A=
Sin A=
Your answer
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
Explanation:The trigonometric functions are very important in math and physics. Sound, light and electricity all involve oscillations and are modeled by sine and cosine functions. So, we can provide a trig ratio for the sine and cosine function by taking a right triangle as shown in the figure below. So the relationships are as follows:
[tex]sinA=\frac{Opposite \ side}{Hypotenuse} \\ \\ cosA=\frac{Adjacent \ side}{Hypotenuse} \\ \\ \\ For \ the \ figure: \\ \\ a:Opposite \ side \\ \\ b:Adjacent \ side \\ \\ c:Hypotenuse[/tex]
So we can write:
[tex]\boxed{sinA=\frac{a}{c}} \\ \\ \\ \boxed{cosA=\frac{b}{c}}[/tex]
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Rewrite the following as a mix numbers 17/3
answer is 5 2/3.............
Answer:
5 2/3
Step-by-step explanation:
Match the following items by evaluating the expression for x = -2.
x-2
x-1
x0
x1
x2
By substituting x = -2 in each expression, we find that x-2 equals -4, x-1 equals -3, x₀ equals 1, x₁ equals -2, and x₂ equals 4.
Explanation:To solve this, we need to substitute x = -2 into each expression. Here are the results:
For x-2, substituting -2 would give us -2 - 2 which is -4.In the expression x-1, substituting -2 would provide us with -2 - 1, which equals -3.For x₀, any non-zero number to the power of zero is 1.When we put -2 into x₁, we simply get -2.Finally, for x₂, -2 squared equals to 4.Learn more about Evaluating expressions here:https://brainly.com/question/21469837
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30 divided by 18 into improper fraction
Answer:
5/3
Step-by-step explanation:
30/18
you can easily simplify a large improper fraction by finding a common number.
in this case the number is 6.
6x5=30 & 6x3=18
therefore, if you divide each number by 6 you get 5/3
decimal: 1.66667 or 1.67 or 1.7
improper fraction: 5/3
proper fraction 1 2/3
Final answer:
30 divided by 18 as an improper fraction is ⅓, or 5/3, obtained by converting the division result into a mixed number and then back into an improper fraction.
Explanation:
To convert 30 divided by 18 into an improper fraction, you first divide 30 by 18 to get the decimal form, which is approximately 1.666. To express this as an improper fraction, we recognize that 1.666 is 1 and 2/3 in mixed number form.
Since 2/3 is already a fraction, we can convert the mixed number back into an improper fraction by multiplying the whole number 1 by the denominator 3 and then adding the numerator 2. This gives us 3 + 2 = 5, so the improper fraction is 5/3.
+5x+3.
What are the factors of the polynomial?
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
2x^2 + 5x + 3
What are the factors of the polynomial?
(2x+3)(x+1)
(2x-3)(x-1)
(3x+2)(x+1)
(3x-2)(x-1)
Answer:Option A
The factors are:
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Solution:Given that, the quadratic equation is:
[tex]2x^2 + 5x + 3[/tex]
We have to find the factors of polynomial
Find the factors:[tex]2x^2+5x+3[/tex]
Split 5x as 2x and 3x
[tex]2x^2+5x+3 = 2x^2 +2x + 3x + 3[/tex]
[tex]\mathrm{Break\:the\:expression\:into\:groups}[/tex]
[tex]2x^2+5x+3=\left(2x^2+2x\right)+\left(3x+3\right)[/tex]
[tex]\mathrm{Factor\:out\:}2x\mathrm{\:from\:}2x^2+2x\mathrm{:\quad }2x\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + (3x+3)[/tex]
[tex]\mathrm{Factor\:out\:}3\mathrm{\:from\:}3x+3\mathrm{:\quad }3\left(x+1\right)[/tex]
Thus we get,
[tex]2x^2+5x+3 = 2x(x+1) + 3(x+1)[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x+1[/tex]
Thus we get,
[tex]2x^2+5x+3 = (2x+3)(x+1)[/tex]
Thus the factors are found for given polynomial
Final answer:
The correct factors of the polynomial +5x+3 are (2x+3)(x+1), as they multiply to give the original polynomial. None of the other provided options yield the correct polynomial upon multiplication.
Explanation:
The question asks to identify the factors of the polynomial +5x+3. Factors are expressions that, when evaluated, produce the value of the polynomial. Let's examine the provided options to find which pair of binomials gives us the correct polynomial upon multiplication:
(2x+3)(x+1) = 2x² + 2x + 3x + 3 = 2x² + 5x + 3, which matches the original polynomial.
(2x-3)(x-1) = 2x² - 2x - 3x + 3 = 2x² - 5x + 3, which does not match the original polynomial.
(3x+2)(x+1) = 3x² + 3x + 2x + 2 = 3x² + 5x + 2, which does not match the original polynomial.
(3x-2)(x-1) = 3x² - 3x - 2x + 2 = 3x² - 5x + 2, which does not match the original polynomial.
Therefore, the correct factors of the polynomial +5x+3 are (2x+3)(x+1).
Passing through (-6, -1) and PARALLEL 2x + 3y = 3
Answer:5
Step-by-step explanation:
The expression 210,000\left(1.02\right)^x210,000(1.02)
x
models the estimated home value after x years. Which statement is the correct representation of the 1.02 in the expression?
The house has a starting value of 1.02.
The house is decreasing in value by 2% each year.
The house is increasing in value by 2% each year.
The value of the house is changing by 0.02% each year.
Answer:
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
Step-by-step explanation:
For this case if we have this expression
[tex] 210000(1.02)^x[/tex]
We have the same functional forma like the exponential model given by:
[tex] y = a b^x[/tex]
Where a = 210000 represent the constant or initial value and b = 1.02 represent the base.
So let's analyze the possible options:
The house has a starting value of 1.02.
False the starting value for this case is 210000 since if x=0 then we see that the value is 210000
The house is decreasing in value by 2% each year.
False the increase is 1.02 each year so then in % we have
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
We have an increase of 2% each year
The house is increasing in value by 2% each year.
Correct the increase is 1.02 per year the value of b>0 and the percentage of increase each year is:
[tex] \frac{1.02-1}{1} *100 = 2\%[/tex]
The value of the house is changing by 0.02% each year.
False the increase is 2% per year
question for class 4