Answer:
[tex]x = 21 - 2\frac{1}{3}y[/tex]
Step-by-step explanation:
3x + 7y = 63
Minus 7y from both sides, then you get...
3x = 63 - 7y
Now we divide both sides by three to find the value of x:
[tex]x = 21 - 2\frac{1}{3}y[/tex]
[tex]x + 49 \ \textgreater \ 28[/tex]I need it now please
To solve an inequation for x you have to follow the same procedure you follow when solving equations, with exception that when you multiply/divide by a negative number the direction of the inequality gets inverted.
So to solve the given inequelity for x, you have to pass "+49" to the other side of the expression. To do so, subtract it from both sides of the expression:
[tex]\begin{gathered} x+49-49>28-49 \\ x>-21 \end{gathered}[/tex]The result of the inequality is x > -21
1. What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)
How to determine the center of the hyperbola?From the question, the equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
As a general representation, a hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
From the above general representation, the coordinates of the center of the hyperbola is
Center = (h, k)
By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we have the following representstion
(h, k) = (2, -3)
This means that
Center = (2, -3)
Hence, the center is (2, -3)
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Answer:
(2,-3) See question 10
Step-by-step explanation:
HELP ME PLEOPLE THIS IS SO CONFUSING HELP ME I WILL GET SUSPENDED IF I DON"T ANSWER THIS HELP ME PLEASE HELP I WILL GET A 0 AND SUSPENDED HELP
the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. 1. what proportion of these banks had an interest rate less than 2.5 percent?
The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 2.5
μ = mean = 2.28
σ = standard deviation = 0.37
z-score = (2.5 - 2.28) / 0.37
z-score = 0.22 / 0.37
z-score = 0.5946
To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.5946
By interpolating the values,
probability = 0.724
proportion = 0.724
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You will have $ in ten years if you set aside $500 a year at 10%.
Compound interest: $8,765.58
question
A group of friends’ dinner bill before tax is $122.75. The sales tax rate is 8%. They want to leave an 18% tip after tax. What is their total dinner bill, including tax and tip, rounded to the nearest cent?
Responses
The cost of the total bill for the friends is $154.665.
What is a tax?This implies a levy that's paid to the government by individuals and firms.
From the information, the.group of friends’ dinner bill before tax is $122.75, sales tax rate is 8% and they want to leave an 18% tip after tax.
The total bill will be:
= Cost of food + Tax + Tip
= $122.75 + (8% × $122.75) + (18% × $122.75)
= $122.75 + $9.82 + $22.095
= $154.665
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the mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5000. the distribution of incomes is skewed to the right. suppose that we select samples of size 43. determine whether the sampling distribution for is normal (or approximately normal) and give its mean and standard deviation.
The sampling distribution for is normal (or approximately normal) and give its mean and standard deviation is the mean is $28520 and its standard deviation is $762.5.
The notion of mean is crucial in both mathematics and statistics. The mean is the average or most frequent value among a set of numbers. It is a statistical measure used to determine the median and mode of a probability distribution's central tendency. It's also known as an expected value. Sum of all observations divided by the total observations equals the mean. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are more dispersed when the standard deviation is high.
Given information :
Mean annual income = $28540
Standard Deviation = $5000
Given sample size is n = 43
Sample size doesn't affect the mean, hence the mean remains the same
New mean = $28540
New standard Deviation = Standard Deviation / n^1/2 = 5000/ (43)^1/2
New standard Deviation = 5000/6.5574 = $762.5
Hence, The mean is $28520 and its standard deviation is $762.5
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How do you solve this problem?
The area of the figure given below is 56.6 units² .
In the question ,
a figure is given
where there is one rectangle and two semicircles .
the length of the rectangle is given as 11 units
and the breadth of the rectangle is = 4 units
we know that the area of the rectangle is = length × breadth
on substituting the values ,
we get
area = 11 × 4
area = 44 units²
the radius of the semicircle = 2 units
the are of the semi circle = (1/2)*π*r²
since there are two semicircle , the area of the two semi circle will be
= 2 * (1/2)πr²
= π*r²
On substituting , the value of radius = 2 ,
we get the area is = 3.14*(2)² = 12.56 using π = 3.14
so the area of the complex figure is = 44 + 12.56 = 56.56
≈ 56.6
Therefore , The area of the figure given below is 56.6 units² .
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What is the answer for the equation:
7x+31 = 8x -1/3(27x+3) ?
The answer for the equation:
7x+31 = 8x -1/3(27x+3) is x=-4
andrea wants to cut a board into three pieces the board is 3 2/3 feet long how long will each piece be
Answer:
7/6 feet
Step-by-step explanation:
The board is 3 and 1/2 feet long, so it is 3+(1/2) feet long.
3 + 1/2 = ?
3/1 + 1/2 = ?
6/2 + 1/2 = ?
(6 + 1)/2 = ?
= 7/2
3 + 1/2 = 7/2
In other words, the board is 7/2 feet long.
Now we have to divide by 3 since Andrea is cutting the board in three pieces.
So:
(7/2)/3 or (7/2) ÷ 3 or [tex]\frac{\frac{7}{2}}{3}[/tex] or (7/2) × (1/3)
= 7/(2×3)
= 7/6
So we found that each piece (after cutting the board into three pieces) is 7/6 feet long.
Sandra purchased $1,200 worth of electronic equipment on her new credit card, with an annual interest rate of 14.99%. If she has no other charges on the card and does not pay off the balance at the end of the month, how much money will she owe the credit card company after 1 month? Estimate the interest using the monthly periodic rate.
Given data:
The given amount of equipment purchased by the Sandra is A=$1,200.
A bank features a savings account that has an annual percentage rate of r=2.8% with interest. compounded quarterly. Benicio deposits $8,000 into the account.
Explanation
From the given question
We are given the formula to compute the amount that a sum of $8000 compounded quarterly will yield after time t at a rate of 2.8%
The formula is given by
[tex]A(t)=a(1+\frac{r}{k})^{kt}[/tex]Part A
[tex]\begin{gathered} a=initial\text{ deposit= \$8000} \\ \\ k=number\text{ of times compounded in a year = 4} \\ \\ r=2.8\text{ \% =0.028} \\ \\ \end{gathered}[/tex]part B
the amount in the account after 7 years will be
[tex]\begin{gathered} A(t)=8000(1+\frac{0.028}{4})^{4\times7} \\ \\ A(7)=\text{ \$}9725.57\text{ } \end{gathered}[/tex]The amount that will be in the account after 7 years will be $9725.57
Part C
APY is given by
In our case we have
[tex]\begin{gathered} APY=(1+\frac{r}{k})^k-1 \\ APY=\left(1+\frac{0.028}{4}\right)^4\:-1 \\ APY=1.02829-1 \\ APY=0.02829 \end{gathered}[/tex]Hence, we will have the APY as
[tex]\begin{gathered} APY=0.02829\times100\text{ \% } \\ APY=2.829\text{ \%} \end{gathered}[/tex]Hence, the APY is 2.829%
True or False: The set of whole numbers is closed under multiplication.
Explanation:
Take any two whole numbers you want. Multiplying them together always result in some (other) whole number.
Examples:
2*3 = 65*7 = 3511*12 = 132In other words,
(whole number)*(whole number) = whole number
This is why we consider the set closed under multiplication.
The line perpendicular to y=1/2x-2 that passes through the point (0,3)
⇒For perpendicular lines when their gradients are multiplied they have to give -1, in this case we are given a line with gradient [tex]\frac{1}{2}[/tex] meaning the gradient of the line perpendicular to it will be -2 since
[tex]-2*\frac{1}{2} =-1[/tex] this means that the gradient of the new line will be -2
⇒Now we have a point and gradient.
⇒And we know that the general equation for a straight line is y=mx+c
[tex]3=-2(0)+c\\3=c\\c=3[/tex]
The equation of the line perpendicular to the given one is
y=-2x+3
GOODLUCK!!
the radius of a right circular cone is increasing at a rate of 5 inches per second and its height is decreasing at a rate of 4 inches per second. at what rate is the volume of the cone changing when the radius is 50 inches and the height is 10 inches?
The rate at which the volume of the cone is changing is -5235.98 inches³/s when the radius of the circular cone is 50 inches and the height is 10 inches.
The formula for the circular cone can be given as;
V = 1/3 πr²h
Now we take the derivative with respect to time as follows;
V = 1/3 πr²h
dV/dt = 1/3π d/dt(r²h)
dV/dt = 1/3π [2r(dr/dt) × h + r²(dh/dt)]
Now we substitute the values in this equation as follows;
dV/dt = 1/3π [2 × 50 × 5 × 10 + (50²) (-4)]
dV/dt = 1/3π [ 5000 - 10000]
dV/dt = 1/3π [-5000]
dV/dt = -5235.98
Hence the negative sign indicates that the volume is decreasing over time and the rate of change is calculated to be -5235.98 inches³/s.
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WILL GIVE BRAINLIEST find center, vertices, and foci of the ellipse.
passes through (1,4) and perpendicular to y=2x-7
The equation of the line is found as y = -x/2 + 9/2.
What is meant by the equation of the line?This is an x and y equation for whom solution set is just a line in the (x,y) plane. The "slope-intercept" form is the most commonly used in algebra. y = mx + b. In effect, x is used as a parameter, and y is written as just a function of x: y = f(x) = mx+b.For the given question;
The equation of the perpendicular line is given as;
y = 2x - 7
Compare the equation with the standard form of slope intercept.
y = mx + c
m = slope and c is the y intercept.
m1 = 2
Now, the line is perpendicular, thus the relation between both slopes is;
m1 × m2 = -1
m2 = -1/2
The passing coordinates of the line is (1. 4).
Find the equation using formula.
y - y1 = m2(x - x1)
y - 4 = (-1/2) (x - 1)
Simplifying,
y = -x/2 + 9/2
Thus, the equation of the line is found as y = -x/2 + 9/2.
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How many times larger is (1.76 x 10^1) than (8 x 10^-1)
Answer:
14.7 times bigger is (1.176 x 10¹) than (8 × 10-¹) if the numbers are (1.176 x 10¹) than (8 × 10-¹).
Step-by-step explanation:
Answer:
22
Step-by-step explanation:
To compare numbers this way, we divide.
(1.76 × 10^1) / (8 × 10^-1) =
= 1.76/8 × 10^1 / 10^-1
= 0.22 × 10^(1 - (-1))
= 0.22 × 10^2
= 22
15 points to help me out.
Answer:
can't answer the first two questions as figure is not mentioned in picture
3. -3
4. 6
5. 3/4
6. -3
7. 5
8. 3
Step-by-step explanation:
Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches. What is the length of the pegboard?
The length of the rectangular pegboard is 80 inches
What is a rectangle?A rectangle is a polygon with four sides in which two opposite sides are parallel and equal
How to find the length of the rectangular pegboard?Since Vince is cutting a rectangular piece of pegboard to use in his garage for organization. The width of the pegboard is 8 inches less than half the length. The perimeter of the pegboard is 224 inches.
Let
L = length of pegboard and W = width of pegboard.Since the width of the pegboard is 8 inches less than half the length, we have that
W = L/2 - 8
Also, since the pegboard is a rectangle, its perimeter, P = 2(L + W)
Now, its perimeter P = 224 inches.
So, 2(L + W) = 224
L + W = 112
Now, substituting the width, W into the equation, we have
L + W = 112
L + L/2 - 8 = 112
L + L/2 = 112 + 8
L + L/2 = 120
3L/2 = 120
L = 120 × 2/3
L = 240/3
L = 80 inches
So, the length of the pegboard is 80 inches
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please help me , and can you explain what i shluld study to understand this
x = 12° and y = 7° are the value of linear angles.
What is linear pair of angles?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's angles add up to 180° in all cases.8x° = 96°
x = 96/8
x = 12°
8x° = 11y + 19
8 * 12° = 11y + 19
96 = 11y + 19
11y = 96 - 19
11y = 77
y = 77/11
y = 7°
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-20 less than or equal to 4x
We will have the following:
[tex]-20\le4x[/tex]When we solve for x we will have
[tex]-\frac{20}{4}\le x\Rightarrow-5\le x[/tex]So, x is equal or grater than -5.
. Represent Real World Problems Lorena and Benita are saving
money. They began on the same day. Lorena started with $40. Each
week she adds $8. The graph describes Benita's savings plan. Which
girl will have more money in 6 weeks? How much more will she
have? Explain your reasoning.
We need to know how to read a graph inorder to solve the problem. At the end of 6 weeks, Lorena will have more money, she will have $8 more than Benita.
We know that Lorena started with $40 and she added $8 every week. We need to find out the final amount she has at the end of 6 weeks. For Benita, we can see from the graph that she started with $50, since the graph starts from $50, and if we observe the amount after every week we can see that she adds $5 every week to the savings. We can directly say from the graph that the final amount Benita has after 6 weeks is $80.
amount Lorena has after 6 weeks = 40+ (6x8)=40+48=$88
Therefore we can see that Lorena will have more money after 6 weeks and she has $8 more than Benita.
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If p and q are integers and pq +p is an odd number, which of the following numbers must be even?
1-p
2-q
3- pq-3
4- p^2
Answer:Answer: number 2 is correct
Ms. lange drove about 150kms east from la sarre, to senneterre, quebec. she drove another 75kms north to lebel-sur-quevillon, what is the approximate air distance from la sarre to lebel-sur-quevillon
The approximate air distance from La Sarre to Lebel-sur-Quevillon is 167.71 km.
To determine the air distance from La Sarre to Lebel-sur-Quevillon, analyze the path she has traveled.
When she drove east and drove another north, the total path she ave traveled is similar to the sides of a right triangle, where the distance from the start and end point is the hypotenuse. (see photo attached)
Using Pythagorean theorem, solve the distance from La Sarre to Lebel-sur-Quevillon.
c² = a² + b²
where a = 150 km and b = 75 km
distance² = 150² + 75²
distance² = 22500 + 5625
distance² = 28125
distance = 167.71 km
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according to a survey of advanced curriculum high school students, the mean time spent studying each day is 6.4 hours. assume the standard deviation is 0.80 hours and that the probability distribution is normal. what is the 80th percentile for number of hours spent studying each day? round your answer to 2 digits after the decimal.
The 80th percentile for the number of hours spent studying each day is 7.07 hours.
A data set with a normal distribution has the majority of its values clustered in the middle of the range, while the remainder taper off symmetrically toward either extreme. The term "standard deviation" refers to the degree of dispersion of the data from the mean. Data are grouped around the mean when the standard deviation is low, and are dispersed when the standard deviation is high.
The percentage of scores below a given value is shown by percentiles. They provide information about how a score compares to other scores.
Given Data :
Mean time (u) = 6.4 hour
Standard Deviation = 0.80 hour
It is given that the probability distribution is normal.
The formula for the z-score is z =( x- mean)/standard deviation
For the 80th percentile, the z value from the z table is 0.842.
We have,
0.842 = (x - 6.4)/0.8
0.842*0.8 = x - 6.4
0.6736 =x - 6.4
x = 0.6736 + 6.4
x = 7.0736
x = 7.07
Hence, the 80th percentile for the number of hours spent studying each day is 7.07 hours.
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Find the volume of this object.Use 3 for π.Volume of a CylinderV= πr²h4 ft9 ft5 ft5 ft5 ftVolume of aRectangular PrismV = whV ≈ [?]ft³Enter
Mathematics → Solid Figures → Volume
The volume of a cylinder is:
[tex]V=\pi r^2h[/tex]In this question,
r = 2 ft (4/2 =2)
h = 5 ft
Then, the volume of the cylinder is (Vc):
[tex]\begin{gathered} Vc=\pi *2^2*5 \\ Vc=\pi *4*5 \\ Vc=20\pi \end{gathered}[/tex]Using π = 3:
[tex]\begin{gathered} Vc=3*20 \\ Vc=60ft^3 \end{gathered}[/tex]The volume of a rectangular prism (Vr) is:
[tex]Vr=lwh[/tex]In this question:
l = 9 ft
w = 5 ft
h = 5 ft
Then, the volume of the rectangular prism is:
[tex]\begin{gathered} V=9*5*5 \\ V=225ft^3 \end{gathered}[/tex]The volume of the object (V) is the sum of the volumes:
[tex]\begin{gathered} V=Vc+Vr \\ V=60+225 \\ V=285ft^3 \end{gathered}[/tex]Answer: 285 ft³.
answer all ........................................................................................................................................................................................................................................................................................................................................1
Answer:
1. 39, 46
2. 180
Step-by-step explanation:
1. count up by 7
2. not sure..
y+1=3/2(x-1) in slope intercept form
Answer:
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
To get slope intercept form (y=mx+b), simplify and solve for y.
y+1=[tex]\frac{3}{2}[/tex](x-1)
Simplify
y+1=[tex]\frac{3}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
Solve for y
y=[tex]\frac{3}{2}[/tex]x - [tex]\frac{5}{2}[/tex]
the sum of the digits in a three digit mumber is 9. the tens digit is half the sum of the other two amd the hundreds digit is half the unit digit. fond the number.
The number is 234.
Step-by-step explanation:
Let the 3 digits be H , T and U so the number is HTU.
H + T + U = 9
T = 0.5H + 0.5U
U = 2H
So from the last 2 equations
T = 0.5H + 0.5(2H)
T = 0.5H + H
T = 1.5H
So substituting for T and H is the first equation:
H + 1.5H + 2H = 9
4.5H = 9
H = 2.
So T = 1.5*H = 1.5 *2 = 3.