Eric took $7000 of his income last year and invested it, part at 7% and the rest at 9%. He earned $570 from investments. How much did he invest at each rate?
Answer:
He invested 3,000 at 7% and 4,000 at 9%.
Step-by-step explanation:
From the information given, you can write the following equations:
x+y=7,000 (1)
0.07x+0.09y=570 (2)
You can solve for x in (1)
x=7,000-y (3)
Now, you can replace (3) in (1) and solve for "y":
0.07(7,000-y)+0.09y=570
490-0.07y+0.09y=570
0.02y=80
y=80/0.02
y=4,000
Finally, you can replace the value of "y" in (3):
x=7,000-4,000
x=3,000
According to this, the answer is that he invested 3,000 at 7% and 4,000 at 9%.
A construction company has eight boxes of shingles with one thousand shingles in each stack. if they need 50000 shingles, do they have enough? Explain how you know
What is the top of the flag pole above ground in inches?
Answer:
13ft 10.2in
Step-by-step explanation:
First let's convert 3ft to in.
3 * 12 = 36 in
Now let's find the angle
We use tangent because we know the opposite and adjacent distances.
tan x = 36/13
tan x = 2.7692
On your calculator, input the value of your tangent. Then press "inv." This should give you the angle associated with that value. The angle associated with tan 2.7692 is 70.14 degrees.
Now that we know the angle we can find the height.
We use tangent again.
tan 70.14 = x / 5 We don't know the opposite but we know the adjacent length is 5ft.
2.77 * 5 = x
13.85 ft = x
To get it in ft and inches multiply .85 by 12
.85 * 12 = 10.2
13ft 10.2in
The aircraft A330 flies at an average speed of 600 miles per hour. The expression, 600t gives the distance traveled by the aircraft in t hours. Find the distance traveled by the A330 in 3 hours.
Answer:
1800
Step-by-step explanation:
The equation 600t is multiplication (600 x t). Since t represents hours, and they're asking you to solve for 3 hours, all you have to do is multiply 600 x 3, which will get you your answer of 1800.
Help with the below image… Thank you!
Answer: third one
Step-by-step explanation:
Answer:
alternate ext angles are <4 <5
will mark BRAINLIEST and give ALL OF MY POINTS!!! Pls help asappp!!!! Tysm!
Answer:
$125$65, $65, $65 -- they are all the sameStep-by-step explanation:
The quantity of food required for the two cats for one day is ...
(3/4 can) + (1/2 can) = (3/4 +2/4) can = 5/4 can
Then the cost per day for cat food is ...
$5/(3 cans) × (5/4 can/day) = $25/12 /day
We note that the cost for some number of days will be the product of this factor and the number of days, rounded up to the next higher $5.
1. The cost for 60 days is ...
(60 days)($25/12 /day) = $25 × 60/12 = $125
A 60-day supply of cat food costs $125.
__
2. A 29-day supply costs ...
(29 day) × $25/12 /day = $60 5/12, rounds up to $65 for 29 days
A 30-day supply costs ...
(30 day) × ($25/12 /day) = $62.50, rounds up to $65 for 30 days
A 31-day supply costs ...
(31 days) × ($25/12 /day) = $64 7/12, rounds up to $65 for 31 days.
These costs are all the same.
_____
3 cans last, on average, 2 2/5 days. That means some purchases of 3 cans will last for 2 days, and some will last for 3 days. It so happens that the purchase made to cover day 29 will also cover day 30 and day 31.
What number is greater than -8 and less than 0.
graph the piecewise function
show how you got the function
(4). If we break down this piecewise function, we have 3 main expressions to deal with, 'h(x) = 5 if {x ≥ 4}' (represented by the green graph) 'h(x) = x if {0 ≤ x ≤ 4}' (represented by the blue graph) and 'h(x) = 1 / 2x + 2 if {x < 0}' (represented by the red graph).
Take a look at the attachment below for your graph of these 3 functions / expressions.
(5). For this part we want to determine the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3]. Remember that to calculate average rate of change between the 2 points we use the following formula...
f(b) - f(a) / b - a,
f(3) = 4(3)² - 5(3) - 8 = 4(9) - 15 - 8 = 36 - 15 - 8 = 13,
f(- 2) = 4(- 2)² - 5(- 2) - 8 = 4(4) + 10 - 8 = 16 + 10 - 8 = 18
13 - 18 / 3 - (- 2) = - 5 / 5 = - 1
Therefore the average rate of change of the function f(x) = 4x² - 5x - 8 over the interval [- 2,3] will be - 1.
. In double integration , we keep one variable say x fixed and _______ a. Reliable the order variable y b. Varying the order variable y
Answer:
A double integral can be written as:
[tex]\int\limits {f(x, y)} \, dx dy[/tex]
Now, to do this integral, we first can fix one of the variables, like in this case, we can fix x.
Now, with x fixed, this will be a function of only one variable, y, then we can do the integration over y.
Once the function is integrated over y, we can now do the integration over x.
Then the correct option will be:
" Varying the order variable y"
We keep x fixed, and integrate over the other variable.
The accompanying data are the shoe sizes and heights (in inches) of 14 men. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not.
(a) x= 11.5
(b) x= 8.0
(c) x = 15.5
(d) x = 10.0
Complete question :
Data of shoe sizes :
X:
8.5
9.0
9.0
9.5
10.0
10.0
10.5
10.5
11.0
11.0
11.0
12.0
12.0
12.5
Height (y) :
66.5
68.5
67.5
70.0
70.0
72.0
71.5
70.0
71.0
71.5
73.0
73.5
74.0
74.0
Answer:
Kindly check explanation
Step-by-step explanation:
Using the online regression calculator :
The regression model obtained in the form:
ŷ = mx + c is ;
ŷ = 1.792X + 52.176
Where ŷ is the predicted or dependent variable
m = 1.792 is the gradient or slope of the regression line
x = the independent variable
c = 52.176 = intercept, where the line of best fit intersects the y axis.
Given the following x values, predict ŷ
(a) x= 11.5
ŷ = 1.792(11.5) + 52.176 = 72.784
(b) x= 8.0
ŷ = 1.792(8.0) + 52.176 = 72.784 = 66.512
(c) x = 15.5
ŷ = 1.792(15.5) + 52.176 = 79.952
(d) x = 10.0
ŷ = 1.792(10.0) + 52.176 = 70.096
The predicted values are meaningful as they show are very close to the actual values of height (y). This could be attributed to the high correlation Coefficient of 0.9299 which exists between both variables
Which is a negatively skewed distribution?
Answer:
The answer is D
Step-by-step explanation:
One this to remember when doing it is that all negatively skewed graphs or plots will always have the outlier that is on the left of the rest
Please Help! I'm stuck
Answer:
D) 11/16
Step-by-step explanation:
Here are the possible combinations she could pull out.
1,1 - 1,4 - 1,5 - 1,8 - 4,1 - 4,4 - 4,5 - 4,8 - 5,1 - 5,4 - 5,5 - 5,8 - 8,1 - 8,4 - 8,5 - 8,8
There are 16 possible combinations. 11 would be above 7, so it’s 11/16.
$1000 invested with compound interest at a rate of 15% per year for 9 years. Formula: M = P(1+ i)n Group of answer choices $3517.88 $424.36 $1519.38 $888.15 $1788.14
Answer:
Option A.
Step-by-step explanation:
Note: Let as consider, we have to find the total amount after 9 years.
It is given that,
Principal amount = $1000
Rate of compound (yearly) interest = 15% = 0.15
Time = 9 year
The formula for total amount is
[tex]M=P(1+i)^n[/tex]
where, P is principal, i is rate of interest and n is number of years.
Substituting P=1000, i=0.15 and n=9, we get
[tex]M=1000(1+0.15)^9[/tex]
[tex]M=1000(1.15)^9[/tex]
[tex]M=1000(3.5178763)[/tex]
[tex]M=3517.8763[/tex]
[tex]M\approx 3517.88[/tex]
So, the total amount after 9 years is $3517.88.
Therefore, the correct option is A.
Which angle is supplementary to 65 degrees
Answer: 115
Step-by-step explanation: Supplementary angles add to 180, so 180-65 = 115
Answer:
115 degrees
Step-by-step explanation:
A supplementary angle is an angle that add up to 180 degrees
Because of the this we can create an equation that solves for x
65 + x = 180
x = Missing angle measure
All you have to do to solve for x is to subtract 65 from both sides, making x 115
Evaluate the variable expression when -= 6, b= 5, and c= -3
Answer:
34
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
(b - 2a)² + bc
Step 2: Define variables
a = 6
b = 5
c = 3
Step 3: Plug in
(5 - 2(6))² + 5(-3)
Step 4: Multiply
(5 - 12)² - 15
Step 5: Parenthesis
(-7)² - 15
Step 6: Exponents
49 - 15
Step 7: Subtract
34
if you are dealt 4 cards from a shuffled deck of 52 cards find the probability that all 4 are hearts
Answer:
Probability of getting 4 hearts = 11/833
Step-by-step explanation:
Find:
Probability of getting 4 hearts
Computation:
Probability of getting 1st heart = 13 / 52
Probability of getting 2nd heart = 12 / 51
Probability of getting 3rd heart = 11 / 50
Probability of getting 4th heart = 10 / 49
Probability of getting 4 hearts = [(13 / 52)(12 / 51)(11 / 50)(10 / 49)]
Probability of getting 4 hearts = 11/833
Simplify (x - y + 1) - (x + y - 1).
-2x + 2y
-2y + 2
2y-2
2x - 2y + 2
Answer:
-2y + 2
Step-by-step explanation:
Let's first remove the parentheses. (x - y + 1) becomes x - y + 1 and -(x + y - 1) becomes -x -y + 1. Combine like terms:
x - y + 1 - x - y + 1 = -2y + 2
Answer:
-2y + 2
Step-by-step explanation:
(x - y + 1) - (x + y - 1)
remove ( )
= x - y + 1 - x - y + 1
simplify
= -2y + 2
Given the following functions: f(x) = x^2 g(x) = x - 3 Find the composition of the two functions and show your process: g(f(x))
Answer:
x^2-6x+9
Step-by-step explanation:
for f=x^2 subsititude x with g(x) = x-3 in which will give you (x-3)^2 using the perfect square formula ((a-b)^2=a^2-2ab+b^2) in which a=x, b=3. you shall then get x^2 -2x · 3 + 3^2 to get x^2-6x+9
if any two ordered pair (2x-3,6)=(x+1,2y/3) find the value of x and y
Answer:
2x-3= x+1
or, 2x- x = 1+3
or, x = 4
so, x = 4
NOW,
6= 2y/3
or, 6×3 =2y
or, 18/2 = y
so, y = 9
X = 4 and Y = 9
ANS
Please help me out ASAP
Answer:
[tex]26^9[/tex]
Step-by-step explanation:
[tex]26^1 *26 ^8\\=26^{1+8} \\=26^{9}[/tex]
solve for slope y=4x+6
Answer:
4
Step-by-step explanation:
y = mx+b where m is slope so the slope is 4
Answer:
slope is 4
Step-by-step explanation:
The equation y=mx+b is the linear equation and m represents slope. In this case m is 4
Architectural Design The "rise to run" ratio of the
roof of a house determines the steepness of the roof.
The rise to run ratio of the roof in the figure is 3 to 4.
Determine the maximum height in the attic of the house
if the house is 32 feet wide.
Answer:
12 feet
Step-by-step explanation:
For an inclined roof, the rise is the vertical distance from the roof rafter to the vertical top plate while the run is the distance from the edge of the wall to half of the center of the ridge.
The slope is the ratio of the rise to run. Given a rise to run ratio of 3 to 4. The house is 32 feet wide.
The run of the roof = half of the width of the roof = 1/2 × 32 feet = 16 feet
Let the rise of the roof (height of the attic) be x, hence:
rise to run ratio = height of attic/ run of roof
3/4 = x/16
x = 3/4 × 16
x = 12 feet
The height of the attic is 12 feet
In general, what can you conclude about a pair of angles that are both congruent and supplementary?
Answer:
Both angles are right angles.
Step-by-step explanation:
Supplementary angles sum to 180°. Since we know that both angles are congruent, let's call them x and x. We can write the following equation:
x + x = 180
2x = 180
x = 90°
Therefore, we can conclude that both angles are right angles.
Answer:
Angles that are both congruent and supplementary each have a measurement that is equal to 90°.
Step-by-step explanation:
A news report suggested that an adult should drink a minimum of 64 fluid oz of water per day.
Based on this report, determine the minimum amount of water an adult should drink, in pints,
per day. (1 pint= 16 fl oz)
Answer:
4 pints
Step-by-step explanation:
Because 16x4=64
Taho earns his regular pay of $11 per hour for up to 40 hours of work per week. For each hour over 40 hours of work per week, Taho earns 1 times his regular pay. How much does Taho earn in a week in which he works 50 hours? A. $550 B. $605 C. $625 D. $750 E. $825
d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6?(
The question is incomplete. Here is the complete question.
(a) How many three-digit numbers can be formed from the digits 0,1,2,3,4,5 and 6, if each digit can be used only once?
(b) How many of these are odd numbers?
(c) How many are greater than 330?
Answer: (a) 180
(b) 75
(c) 105
Step-by-step explanation:
(a) In the group, there are 7 digits. A three-digit number can not start with zero, otherwise, it will be a 2-digit number. So:
For the hundreds position, there are 6 choices.
For the tens position, since the digit can be used only once, there are 6 choices.
For the unit position, there are 5 choices.
The total three-digit number formed is: 6*6*5 = 180
(b) To form an odd number, the unit position must be an odd digit, then:
unit position has 3 choices;
hundreds position has 5 choices;
tens position has 5 remaining choices.
The total three-digit odd number is: 3*5*5 = 75
(c) The number formed must be greater than 330, so:
If the number start with a 3, to be greater, there are 3 other choices (4, 5 and 6), so Tens position has 3 choices and Unit position has 5 choices.
Total number is: 3*5 = 15
Another possibility is the number starts with a digit bigger than 3 and so, there are 3 choices.
Tens position has 6 choices;
Unit position has 5 choices;
Total possibilities are: 3*6*5 = 90
The total number of ways a three-digit number is greater than 330 is:
90 + 15 = 105
Among the seven nominees for two vacancies on a city council are three men and four women. In how many ways can these vacancies be filled
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
c) with one of the men and one of the women?
Answer:
a) 21 ways
b) 6 ways
c) 12 ways
Step-by-step explanation:
We solve this question using combination formula
C(n, r) = nCr = n!/r! (n - r)!
a) with any two of the nominees?
Probability (two of the nominees) = 7C2
= 7!/2! ×(7 - 2)!
= 7!/ 2! × 5!
= 7 × 6 × 5 × 4 × 3 × 2 × 1/2 × 1 ×(5 × 4 × 3 × 2 × 1)
= 21
b) with any two of the women?
We have a total of 4 women
Hence, the probability of any two of the four women, filling the vacancies =
P(any two of the women) = 4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 4 × 3 × 2 × 1/ 2 × 1 ×( 2 × 1)
= 6
c) with one of the men and one of the
Total number of men = 3
Total number of women = 4
= 3C1 × 4C1
= [3!/1! ×(3 - 1)! ] × [4!/1! ×(4 - 1)! ]
= [3!/1! × 2!] × [4!/1! ×3!]
= [3 × 2 × 1/ 1 × 2 × 1] × [4 × 3 × 2 × 1/ 1 × 3 × 2 × 1]
= 3 × [24/6]
= 3 × 4
= 12 ways
The probability for any two of the nominees is 21
The probability for two women is 6
This question is incomplete
Complete Question
Among the seven nominees for two vacancies on the city council are three men and four women. In how many ways may these vacancies be filled
a) with any two of the nominees?
b) with any two of the women?
We have given,
Total number of nominees for two vacancy =7
We solve this question using combination formula
What is the formula for combination?
[tex]C(n, r) = nCr = n!/r! (n - r)![/tex]
a) with any two of the nominees?
Total number of nominees(n)=7
We are selecting r nominees r=2
Probability = 7C2
= [tex]\frac{7!}{2! (7 - 2)!}[/tex]
= 7!/ 2! × 5!
= 21
b) with any two of the women?
We have a total number of women=4
Out of 4 we have select 2 women
Hence, the probability of any two of the four women is
4C2
= 4!/2! ×( 4 - 2)!
= 4!/ 2! × 2!
= 6
Therefore,probability for two women is 6
To learn more about the combination visit:
https://brainly.com/question/25821700
Round 7.3564 to the nearest hundredth.
Answer:
7.36
Step-by-step explanation:
7.3564 would round to 7.36
Answer:
7.36
Step-by-step explanation:
To round off a decimal to the hundredths or a number to the right you do this, if the number to the right of the hundredths is 4 or less you remove all the other digits including the hundredths, if the number is 5 or more you add one to the digit in the hundredths.
Help what is the answer help plz
Answer:
2
Step-by-step explanation:
-r^2+5ry+4y^2
= -(-2)^2+5(-2)(3)+4(3)^2
= -(4)+5(-6)+4(9)
= -4-30+36
= 36-30-4
= 36-34
= 2
The distance from home plate to the fence in dead center at the Oak Lawn Little League field is 280 feet. How far is it from the fence in dead center to third base? [Hint: The distance between the bases in Little League is 60 feet.]
Answer:
241.3 feet
Step-by-step explanation:
From the above question, we solve for this using the law of cosines
Law of cosines
a² = b² + c² -2bc Cos A
a = √b² + c² -2bc Cos A
a = The distance between the bases in Little League = 60 feet
b = ???
c = The distance from home plate to the fence in dead center at the Oak Lawn Little League field = 280 feet
A = It makes an angle of 45°
This is because the distance 60 feet and 280 feet are perpendicular to each other and they meet at a point that divides a right angle 90° into equal parts.
a = √280² + 60² - 2 × 280 × 60 × Cos 45
a = 241.33216 feet
Approximately = 241.3 feet
How far is it from the fence in dead center to third base? 241.3 feet