A bank loaned out $25,000, part of it at the rate of 12% annual interest, and the rest at 4% annual interest. The total interest earned for both loans was $1,480.00. How much was loaned at each rate?
Answer:
1875
Step-by-step explanation:
The bank loaned part of the $25,500 at a 6% interest rate. We will call this loan amount x. Then the rest of the 25,500 was loaned at a 9% interest rate. We will define this amount as 25,500 - x. We also know that the total interest earned was $1,875. With this information, we form the equation:
.06(x) + .09(25500 - x) = 1,875
.06x + (2,295 - .09x) = 1,875
Simplify the above equation to:
-.03x + 2,295 = 1,875
-.03x = -420
x = 14,000
Since x is the amount loaned at the 6% interest rate, we know that $11,500 was loaned at a 9% interest rate. (25,500 - 14,000 =11,500)
To figure out the amount loaned at 6%, subtract 11,500 from 25,500 ... this gives us 14,000. This means $14,000 was loaned at 6%.
To check:
14,000 x .06 = 840
11,500 x .09 = 1035
840 + 1035 = 1875
Find the real distinct value
Answer:
Step-by-step explanation:
it has real roots if disc.≥0
p²-4×2×3≥0
p²≥24
|p|≥2√6
p≥2√6
or
p≤-2√6
Evaluate −x+| y | when x=1/3 and y=−7/4. Write your answer as a fraction in simplest form.
−x+| y |=
Answer:
- 25/12
Hope it helps!
please help and give easy to understand explanation.
Answer:
1:2
Step-by-step explanation:
Scale factor of similar figures is usually the ratio of one to the other.
In the diagram given, the scale factor is the length of any side of the smaller figure divided by the length of the corresponding side length of the bigger figure.
Length of smaller figure = 3
Corresponding length of larger figure = 6
Scale factor = smaller figure/larger figure = 3/6
Simplify
Scale factor = ½
I got you :D
help please
Sorry if it’s blurry
which side lengths form a right triangle ?
Answer:
B
Step-by-step explanation:
1^2 + 8^2 = c^2
1 + 64 = c^2
65 = c^2
√c^2 = √65
Coco needs 150mg of a medication that comes in tablets labelled 100mg each. How many tablets will you give her?
Please show work!
Answer:
1.5
Step-by-step explanation:
If 1 tablet is 100mg, and you need 150mg, we set up this equation:
Let x be the number of tablets Coco needs.
x = 150/100
x = 1.5
Therefore, you need 1.5 tablets for the medication.
6.34 Prenatal vitamins and Autism: Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (periconceptional period). (Schmidt, 2011)
Autism Typical Development Total
No vitamin 111 70 181
Vitamin 143 159 302
Total 254 229 483
(b) Complete the hypothesis test and state an appropriate conclusion.
What is the value of the test statistic for this test? ____ (Please round to two decimal places) What is the p-value associated with this test? _____ (Please round to four decimal places)
The test is to find out if there is a difference in the proportion of the number of autism in two samples differentiated by the use of vitamins.
The test statistic for the test is approximately 2.98
The p-value associated is 0.0028
Reasons:
The given parameters are;
[tex]\begin{array}{|l|c|c|c|}&\mathbf{\underline{Autism}}&\mathbf{\underline{Typical \ Development }}&\mathbf{\underline{Total}}\\No \ vitamin&111&70&181\\Vitamin&143&159&302\\Total&254&229&483\end{array}\right][/tex]
The null hypothesis is H₀; [tex]\hat{p}_1 = \hat{p}_2[/tex]
The alternative hypothesis is Hₐ; [tex]\hat{p}_1 \neq \hat{p}_2[/tex]
Where:
[tex]\hat{p}_1[/tex] = The proportion of the sample that did not use vitamin and had autism
[tex]\hat{p}_2[/tex] = The proportion of the sample that used vitamin and had autism
The test statistics for the difference of two proportions is given as follows;
[tex]Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}\cdot (1-\hat{p}) \cdot \left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}[/tex]
Where;
n₁ = 181, n₂ = 302, [tex]\hat p_1 = \dfrac{111}{181}[/tex], [tex]\hat p_2 = \dfrac{143}{302}[/tex], [tex]\hat p = \dfrac{111 + 143}{181 + 302 } = \dfrac{254}{283}[/tex]
[tex]The\ test\ statistics,\, Z=\dfrac{\dfrac{111}{181}-\dfrac{143}{302}}{\sqrt{ \dfrac{254}{283}\cdot (1-\dfrac{254}{283}) \times \left (\dfrac{1}{181}+\dfrac{1}{302} \right )}} \approx 2.98[/tex]
The test statistic for the test, Z ≈ 2.98
From the Z-table, we have Z > 2.98 = 1 - 0.9986, therefore, given that the
alternative hypothesis [tex]\hat p_1 \neq \hat p_2[/tex], the p-value is 2 × (1 - 0.9986) = 0.0028
The p-value associated with the test is 0.0028
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The table below represents a linear function. Find the
value of y when x = 2.
- 2
0
4
6
y
4
8
16
20
Answer:
y = 10x - 6
Step-by-step explanation:
If we know the function is linear then we can use any two coordinate pairs to find the slope of the line.
Note that the first pair is (0, -6) and the last pair is (4, 34). The 'run' is from x = 0 to x = 4, a 'run' of 4. The 'rise' is from -6 to34, a 'rise' of 40. Thus, the slope of this line is m = rise / run = 40/4 = 10.
what is the sequence of 1. 4. 6. 24. 26
Answer:
Multiply by 4, then add 2
Step-by-step explanation:
1*4 = 4
4 + 2 = 6
6*4 = 24
24 + 2 = 26
and so on...
I’ll give 50 points if you can help
Answer:
x = 6 degrees
Step-by-step explanation:
A straight line is 180 degrees and we can make out three angles the form it, this means the three of them add to 180 using the straight angle theorem:
5x + x + 54 + 90 = 180
6x + 144 = 180
6x = 36
x = 6
Li enters a competition to guess how many jelly beans are in a jar.
Li’s guess is 345 jelly beans.
The actual number of jelly beans is 300.
What is the percent error of Li’s guess?
Answer:
15
Step-by-step explanation:
345-300 X 100 = 15%
300
Answer:
Percent error =
15%
Li’s guess was off by
15%.
Step-by-step explanation:
TTM </3
PLEASE HELP NOW!!!! 85 POINTS GIVEN! North America and Eurasia are moving apart due to continental drift. Tanvi calculates that they are doing so at a rate of roughly 2.5×102 centimeters per century. What would be the most appropriate unit for Tanvi to use instead of centimeters per century?
A-centimeters per year B-centimeters per week
C- centimeters per day D-centimeters per hour
Answer:
Answer is option A
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
A. Centimeters per year
Step-by-step explanation:
I THINK. It's easier to think about it when you give shorter amounts of time, but not as short as a day or hour because the movement is too slow
(-8) + (-10) _(-12) =
16 - 24 + 10 =
79 - (-80) + (-15) =
(-5) (-15) (+9) =
(-650) ÷ (+65) + (10) =
Answer:
-30
2
144
675
0
Step-by-step explanation:
A coffee shop currently sells 400 lattes a day at $2.75 each. They recently tried raising the by price by $0.25 a latte, and found that they sold 40 less lattes a day.
Answer:
Steps and solution in the attached picture.
Step-by-step explanation:
Steps and solution in the attached picture.
answer the questin will mark brainlest
-When invested at an annual
interest rate of 7% an account
earned $581.00 of simple
interest in one year. How much
money was originally invested in
account
Answer:
$8300
Step-by-step explanation:
First, you need to know the formula for this type of question.
The formula is I = Prt. These variables are: I = Interest, P = Principle investment, r = Rate, and t = Time.
Your equation will be 581 = P(0.07)(1), since 0.07*1 is 0.07, you'll earn only 7% interest.
So, we broke down the equation to 581 = P(0.07), and you have to isolate P.
Since you have to isolate P, you divide 0.07 from both sides of the equation, which is 581/0.07 = 8300.
So, your principle investment is $8300.
Good luck!
Write your answer in a + bi form.
A=___
B=___
Answer:
Step-by-step explanation:
[tex]\frac{-3+7i}{-6-7i} \times \frac{-6+7i}{-6+7i} =\frac{18-21i-42i-49i^2}{(-6)^2-(7i)^2} \\=\frac{18-63i -49(-1)}{36-49i^2} \\=\frac{18+49-63 i}{36-49(-1)} \\=\frac{67-63i}{36+49} \\=\frac{67-63i}{85} \\=\frac{67}{85} +(\frac{-63}{85} )i\\[/tex]
[tex]a=\frac{67}{85} \\b=\frac{-63}{85}[/tex]
A real estate agent has 10 properties that she shows. She feels that there’s a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute probability of selling no more than six properties in one week
Answer:
Step-by-step explanation:
According to the condition, for any single property the probability not selling it during a week is 100% - 40% = 1 - 0.4 = 0.6.
The probability not selling any one of 13 properties during a week is 0.6%5E13.
The probability to sell at least 1 property in one week is the COMPLEMENT to it
pls pls pls help help help pls this is important to me look at the picture
Answer:
here this should be right
find the square root of 12.96 by divison method
Answer:
3.6
Step-by-step explanation:
HOPE IT HELPS!!!!!!!
Step-by-step explanation:
See this above attachment.
[tex]\tt{\sqrt{12.96}=3.6}[/tex]
Each face of a cube is a square with a side length of 3 meters. What is the total area of all the faces of the cube?
Answer: 54
Step-by-step explanation:
A cube is a perfect square to find the area use L x W and if the length is 3, the width is 9
A cube has 6 sides, so 9 x 6 = 54
The total area of all the faces of the cube is 54 square meters.
Let's dive into finding the total area of all the faces of a cube.
A cube is a special type of three-dimensional shape where all its sides (called faces) are equal squares.
In your case, each face has a side length of 3 meters.
Now, to find the total surface area of the cube, we need to calculate the area of each face and then add them up.
The formula to find the area of a square is side length squared, which is [tex]\(A = s^2\)[/tex], where [tex]\(A\)[/tex] is the area and [tex]\(s\)[/tex] is the side length.
So, for your cube, each face's area is [tex]\(3^2 = 9\)[/tex] square meters. Since a cube has 6 faces,
we simply multiply the area of one face by the number of faces: [tex]\(6 \times 9 = 54\)[/tex] square meters.
To sum it up, the total area of all the faces of the cube is 54 square meters.
This is calculated by finding the area of one face and then multiplying it by the total number of faces.
In this case, each face has an area of 9 square meters, and a cube has 6 faces, resulting in a total area of 54 square meters.
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Question 9 of 10
The two lines below are parallel. If the slope of the red line is what is the
slope of the green line? Use a slash mark (/) as a fraction bar if necessary.
Answer:
if the lines are parallel, that means they have to have the same slope in order to stay parallel to one another. so the slope of both the green and red lines is 1/5
Given f (x) = 5x - 3, find f (-2)
Answer:
f(- 2) = - 7
Step-by-step explanation:
To evaluate f(- 2) substitute x = - 2 into f(x), that is
f(- 2) = 5(- 2) + 3 = - 10 + 3 = - 7
Estimate a 15% tip on a dinner bill of 69.85 by first rounding the bill amount to the nearest ten dollars
Answer:
10.5$
Step-by-step explanation:
Nearest 10 dollar: 70$
since the tip is 15% u take the 15 and divide it by a 100
amd than multiply the answer with 70$
the answer will be 10.5$
PLEASE HELP ME PLS ILL MARK BRAINLIEST
SPAMMERS REPORTED
Answer:
f=-1/3+2 1/3
Step-by-step explanation:
cause do slope equation
For what values of x is f(x) =-2x - 3 increasing? For what
values of x is it decreasing?
Answer:
The value of y is decreasing for all real values of x (-∞,∞).
Step-by-step explanation:
Seeing as we have a simple 1st power equation, the slope will remain the same. So, we solve for slope to see if this equation is for an increasing or a decreasing line.
y = mx + b, where m = the slope of the line
Is the standard slope form of a line, which matches the one given.
so in our equation, f(x) = -2x -3, our m value is -2.
Seeing as -2 is less than 0, the answer is:
The value of y is decreasing for all real values of x (-∞,∞).
Solve for x if line a and b are parellel. SHOW YOUR WORK PLEASE.
Answer:
Step-by-step explanation:
Internal alternate angles are identical when parallel lines are intersected by a third line
3x + 16 = 5x - 54
-2x = -70
x = 35
A classroom board is 36 inches wide and 24 inches tall. Cheryl
is putting ribbon along the outside edge of the board. How
many inches of ribbon will she need?
24 inches
36 inches
A 156 inches B 120 inches
C90 inches
D 60 inches
Answer:
option B
Step-by-step explanation:
The amount of ribbon needed is 120 inches
what is perimeter?The perimeter formula for a rectangle states that P = (L + W) × 2, where P represents perimeter, L represents length, and W represents width.
Given:
length = 24 inches
width = 36 inches
So, amount of ribbon needed
=2(36+ 24)
=2(60)
=120 inches
Hence, the amount of ribbon needed is 120 inches
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What is the midpoint of AC on the grid below?
Answer: Coordinates of the point E of the middle AC (-1 ; 1 )
Step-by-step explanation:
The middle of AC can be calculated by the formula :[tex]\sf \displaystyle M=\left (\frac{x_1+x_2}{2} \ ; \ \frac{y_1+y_2}{2} \right ) =(x_m \ ; \ y _m )[/tex] In our case :A(2 ; 4) ; C(-4 ; -2) Then :[tex]\sf \displaystyle M=\left (\frac{2+(-4)}{2} \ ; \ \frac{4-2}{2} \right ) =(-1 \ ; \ 1 )[/tex] Coordinates of the point E of the middle AC (-1 ; 1 )