Answer: 6 pounds and 12 pounds.
Step-by-step explanation:
1.5(x)+2.4(18-x)=2.1(18)
1.5x+43.2-2.4x=37.8
1.5x+43.2=37.8+2.4x
0.9x=5.4
x=6 pounds of $1.50 candy
18-6=12 pounds of $2.40 candy
(check my work to see if it's correct :))
If Gabe buys 20 yards of fabric, uses 6 2/3 yards to make some pillow cases and another 10 1/4 yards to make curtains for his room, how many yards of fabric will he have left?
Answer:
3 and 1/12 left
Step-by-step explanation:
Kai is swinging on a trapeze in a circus show. The horizontal distance between Kai and the edge
of the stage, in meters, is modeled by D(t) where t is the time in seconds. The function is
graphed below, along with one segment highlighted.
The sinusoidal expression of the function is D(t) = -cos(3t)
What is sinusoidal expression?A sinusoidal alternating current can be represented by the equation i = I sin ωt, where i is the current at time t and I the maximum current. In a similar way we can write for a sinusoidal alternating voltage v = V sin ωt, where v is the voltage at time t and V the maximum voltage.
here, we have to,
to determine the sinusoidal expression:
When he pushes off, he is 1 m behind the center.
This means that:
Amplitude, a = 1.
But we use, a = -1 because he is behind
The graph has a minimum point at (0,-1) and then intersects its midline at (π/6, 0).
So, the period B is: 2π/B = 4 * π/6 and the vertical shift (d) is 0
Simplify 2π/B = 4 * π/6
2π/B = 2π/3
By comparison, we have:
B = 3
The function is given as:
a cos(Bt) + d
Substitute the calculated values
D(t) = -cos(3t)
Hence, the sinusoidal expression of the function is D(t) = -cos(3t)
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Answer:
period and he completes a swing in ten seconds
Maria started an account with an initial deposit of $47.00 on week 1. She then deposited $18.50 into the account each week thereafter for a total of 40 weeks. How much was the balance of the account after 40 weeks?
Answer:
$121.00
Step-by-step explanation:
y = 18.50x + 47.00
y = the total amount in the account
x = the number of weeks
y = 18.50(4) + 47.00
y = 74.00 + 47.00
y = 121
You randomly survey middle school students and high school students about whether they prefer spring or winter. The results
are shown in the two-way table. Find the percent of middle school students that prefer each season and the percent of high school students that prefer each season.
Percentages are:
Middle school
Spring = 75% Winter = 25%
High school
Spring = 40% Winter = 60%
What is the percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Frequently, it is indicated with the per cent sign, "%". A percentage is a number without dimensions and without a standard measurement.
Given,
Middle school
Number of students preferring spring = 93
Number of students preferring winter = 31
High school
Number of students preferring spring = 36
Number of students preferring winter = 54
Total number of middle school students = 93 + 31 = 124
Percentage of middle school students who prefer spring = [tex]\frac{93}{124} * 100[/tex]
= 75%
Percentage of middle school students who prefer winter = [tex]\frac{31}{124} * 100[/tex] = 25%
Total number of high school students = 36+54 = 90
Percentage of high school students who prefer spring = [tex]\frac{36}{90} * 100[/tex]
= 40%
Percentage of high school students who prefer winter = [tex]\frac{54}{90} *100[/tex]
= 60%
Therefore the above is the percentage of students who prefer spring and winter.
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If a seed is planted, it has a 95% chance of growing into a healthy plant.
If 7 seeds are planted, what is the probability that exactly 4 don't grow? Round answer to 4 decimal places.
The probability that exactly 4 out of 7 seeds planted do not grow is 0.0007 (approximately), given that each seed has a 95% chance of growing into a healthy plant.
Calculating the probability of a specific outcome using the binomial distribution formula.The probability that a seed doesn't grow is 1 - 0.95 = 0.05.
To calculate the probability that exactly 4 seeds don't grow out of 7, we need to use the binomial distribution formula, which is:
P(X=k) = C(n, k) * [tex]p^k[/tex] * [tex](1-p)^{(n-k)}[/tex]
where:
X is the random variable representing the number of seeds that don't grow.
k is the specific number of seeds that don't grow (in this case, k=4)
n is the total number of seeds planted (n = 7)
p is the probability that a seed doesn't grow (p=0.05)
C(n,k) is the number of ways to choose k items out of n, also known as the binomial coefficient.
Plugging in the values, we get:
P(X=4) = C(7,4) * 0.05⁴ * 0.95³
= 35 * 0.00000625 * 0.857375
= 0.0006522
Rounding to four decimal places, the probability that exactly 4 seeds don't grow is 0.0007 (approximately).
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what is the slope of (-11,12) and (5,4)
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the following formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the points (-11, 12) and (5, 4), we get:
m = (4 - 12) / (5 - (-11)) = -8 / 16 = -1/2
So the slope of the line passing through (-11, 12) and (5, 4) is -1/2.
Which equation represents a proportional relationship?
y=-x
y = 5x + 1
y = −5 (x + 1)
o y =15x
A faucet gives 20 gallons of water in 5 seconds. How many gallons does it give in 7 seconds?
Answer:
28
Step-by-step explanation:
IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS
CROSS MULTIPLY
Answer:
20 gallons / 5 seconds = 4 gallons / second
Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.
Step-by-step explanation:
*Image*
Find the value of x.
The value of the exterior angle x of the quadrilateral is equal to
How to evaluate for the exterior angle xThe sum of the exterior angles of any convex quadrilateral is 360 degrees so we have that:
65 + 106 + 78 + x = 360
simply the left hand side of the equation
249 + x = 360
subtract 249 from both sides of the equation
249 - 249 + x = 360 - 249
x = 111°
In conclusion, since the sum of the exterior angles of a quadrilateral is s 360°, we have got the measure of one the the exterior angle x to be equal to 111°
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the Green were Planes?
There are 16% of the Green were Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Total number of green planes = 250
The total number of all planes = 1550
The percent of green planes = (number of green planes/number of total planes ) x 100
The percent of green planes = (250/1550) x 100
The percent of green planes = 0.1612 x 100
The percent of green planes = 16.129
Round to the nearest percent, and we get
The percent of green planes = 16%
Thus, 16% of the Green were Planes.
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Please I could really use some help
Answer:
-1/2
Step-by-step explanation:
cos(-360+60)=-1/2
[tex]\cos(\alpha - \beta)= \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ -300\implies 30-330\hspace{5em}\cos(-300^o)\implies \cos(30^o-330^o) \\\\\\ \cos(30^o-330^o)\implies \cos(30^o)\cos(330^o)+\sin(30^o)\sin(330^o) \\\\\\ \cfrac{\sqrt{3}}{2}\cdot \cfrac{\sqrt{3}}{2}~~ + ~~\cfrac{1}{2}\cdot \cfrac{-1}{2}\implies \cfrac{3}{4}~~ + ~~\cfrac{-1}{4}\implies \cfrac{3}{4}-\cfrac{1}{4}\implies \cfrac{2}{4}\implies \boxed{\cfrac{1}{2}}[/tex]
Solve it but using the SQUARE ROOT PROPERTY
please help need ASAP!
The solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
What is quadratic equation?
A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic equation is:
ax^2 + bx + c = 0
where x is the variable, and a, b, and c are constants, with a not equal to 0. The quadratic equation can have two solutions, one solution, or no real solutions, depending on the values of a, b, and c.
Starting with the given equation:
25 = (x + 9)²
We can start by taking the square root of both sides of the equation, which gives us:
±5 = x + 9
Next, we can isolate x by subtracting 9 from both sides of the equation:
x = -9 ± 5
This gives us two solutions:
x = -9 + 5 = -4
or
x = -9 - 5 = -14
Therefore, the solutions to the quadratic equation 25 = (x + 9)² are x = -4 and x = -14.
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Triangle XYZ is shown on the coordinate plane.
A triangle on the coordinate plane with vertices X at 0 comma 5, Y at 10 comma 3, and Z at 4 comma negative 1.
If triangle XYZ is translated using the rule (x, y) → (x + 2, y + 3) and then reflected across the x-axis to create triangle X″Y″Z″, what is the location of Z″?
(2, −8)
(6, −2)
(8, −2)
(12, −6)
The transformation of triangle XYZ vertices at X(0, 5), Y(10, 3), and Z(4, -1), indicates that the coordinate of the point Z'' following a composite transformation of a translation of (x, y) → (x + 2, y + 3), and a reflection across the x-axis, is located at the point (6, -2). The correct option is therefore;
(6, -2)What is a reflection transformation?A reflection transformation is a transformation that produces a mirror image of a geometric figure across a line of reflection.
The coordinates of the vertices of the triangle are;
X(0, 5), Y(10, 3), Z(4, -1)
The transformation rule that is used to translate the triangle ΔXYZ (to get ΔX'Y'Z'), can be presented as follows;
(x, y) → (x + 2, y + 3)The reflection of the translated figure of the triangle (ΔX'Y'Z'), to get ΔX''Y''Z'', is a reflection across the x-axis, therefore, we get;
The coordinates of the point (x, y) following a reflection across the x-axis is the point (x, -y)Therefore, we get the coordinate of the point (x, y) following the composite transformation is the point (x + 2, -(y + 3))
(x, -y) → (x + 2, -(y + 3))The coordinates of the point Y(4, -1) following the composite transformation is therefore;
Y(4, -1) → (4 + 2, -(-1 + 3)) = (6, -2)
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X
7
X
X
Polynomial:
7
X
7x² + 48xy - 7y² is the simplified expression
What is a polynomial?Polynomial is an equation described as the sum of terms in the form of
k[tex]x^n[/tex].
where,
k and n = positive integers.
Example:
2x³ + 4x² + 3x + 5 is a polynomial.
We have,
(x + 7y) (7x − y)
Distribute the addition over subtraction.
x (7x - y) + 7y (7x - y)
7x² - xy + 49xy - 7y²
Add like terms.
7x² + 48xy - 7y²
We can not further simplify.
So,
7x² + 48xy - 7y² is the final expression.
Thus,
7x² + 48xy - 7y² is the simplified expression
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The complete question.
Find the product (x+7y) (7x−y)
A large bamboo plant is 3 times as tall as a small bamboo plant. If the large plant is 16.5 feet tall, how tall is the small bamboo plant?
Answer:
The small bamboo plant is 5.5 feet tall
Step-by-step explanation:
I (1) = 16.5 ft, 3 times as tall as II
II (2) = ? ft
Let the first be x and the second be y, Than
x = 16.5 ft
x = 3y
y = x / 3
y = 16.5 / 3
y = 5.5 ft
Geometry due soon please help!!!!!
In AUVW, u = 6.7 inches, ZW=19° and ZU=5°. Find the area of AUVW, to the
nearest 10th of an square inch.
The required, area of the triangle to the nearest 10th of a square inch is 34.1 square inches.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°
Here,
Calculating unknown angle v,
Since the sum of the angles in the triangle is equal to 180,
u + w+ v = 180
5 + 19 + v = 180
v = 180 - 24
v = 156°
Now,
Calculating the unknown side w,
U/sinu = W/sinw
6.7/sin5° = W/sin19°
W =25.0277
Now,
Area of the triangle is given as
= 1/2 UW sinv
= 1/2× (25.027)×(6.7)×(sin156°)
= 34.1 square inch
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What are the outliers in the data set? How do you know that they are outliers?
Step-by-step explanation:
you have to find your five number summary
A baseball team plays in a stadium that holds 66000 spectators. With the ticket price at $9 the average attendance has been 28000. When the price dropped to $7, the average attendance rose to 33000. Find a demand function D(q), where q is the quantity/number of the spectators. (Assume D(g) is linear) D(q) =
The demand function of the question is expressed as;
D(q) = -²/₅₀₀₀q + 14.6
How to find the Demand Function?The formula to find the slope between two coordinates is;
m = (y2 - y1)/(x2 - x1)
The coordinates we are given are;
(28000, 9) and (33000, 7)
Thus;
Slope; m = (7 - 9)/(33000 - 28000)
m = -2/5000
Now, the equation of a line in point slope form is;
y - y1 = m(x - x1)
Where (x1, y1) is (28000, 9)
y - 9 = (-2/5000)(x - 28000)
y - 9 = -²/₅₀₀₀x + 5.6
y = -²/₅₀₀₀x + 14.6
This can be rewritten as a demand function; D(q) = -²/₅₀₀₀q + 14.6
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The iced tea can is made from a sheet of aluminum that weighs 0.01
ounce per square inch. You receive $0.40 per pound of aluminum that
you recycle. How much do you earn for recycling 24 iced tea cans?
You would earn $0.006 for recycling 24 iced tea cans.
How to find the earning for the recyclingTo determine the amount earned from recycling 24 iced tea cans, we need to find the total weight of the aluminum used in those cans and then convert that weight to pounds.
The total weight of the aluminum used in 24 cans as follows:
24 cans * 0.01 ounce per square inch = 0.24 ounces
Converting ounces to pounds, using a conversion factor of 1/16:
0.24 ounces / 16 ounces per pound = 0.015 pounds
The total amount earned:, since each pound is $0.40
0.015 pounds * $0.40 per pound = $0.006
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Talking on the telephone causes cancer.
6. There are marbles of four different colors in a bag. The
ratio of red to white to blue marbles is 3:4:5. There are half
as many green marbles as there are blue marbles. What is
the least possible number of marbles in the bag?
(A) 12
(B) 24
(C) 29
(D) 58
Answer:
(C) 29
Step-by-step explanation:
Answer:
the least possible number of marbles in the bag is 12.
Step-by-step explanation:
As for the question about the marbles, let's call the number of red marbles "x". Then the number of white marbles is 4x, the number of blue marbles is 5x, and the number of green marbles is (1/2) * 5x = 2.5x.
The total number of marbles in the bag is x + 4x + 5x + 2.5x = 12.5x.
To find the least possible number of marbles, we need to find the smallest possible value of x, which will give us the smallest total number of marbles. Since x represents the number of red marbles, it must be a positive integer. The smallest positive integer value of x is 1.
So, if there is one red marble, there are 4 white marbles, 5 blue marbles, and 2.5 green marbles. The total number of marbles in the bag is 1 + 4 + 5 + 2.5 = 12.5.
Therefore, the least possible number of marbles in the bag is 12.
When put on a coordinate plane, 1st street has the equation y = 6x - 7. 2nd street is parallel to 1st street and
goes through the point (2, 9). Write the equation for 2nd Street in slope-intercept form.
by
The linear equation for the parallel line will be y=6x-3.
What exactly is a linear equation?
The equation is referred to as linear when a variable's maximum power is 1. A one-degree equation is another name for it. A linear equation in one variable has the conventional form Ax + B = 0. This equation has three variables: x, A, and B. A is a coefficient. A linear equation in which there are only two variables typically takes the form Ax + By = C. In addition to the constant C, there are three other constants: the variables x and y, the coefficients A and B, and the variables.
Now,
Line parallel to line y=6x-7 will have same slope which will be m=6
as general equation is y=mx+c where m=slope and c=constant.
For parallel line c will be as it is passing through (2,9)
9=6*2+c
c=9-12
c=-3
then the equation will be y=6x-3
Hence,
The equation for the parallel line will be y=6x-3.
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Help me with this Quadratic function graph the function
The graph of the quadratic function can be seen on the image at the end.
How to graph the quadratic function?The only way to graph or sketch a function by hand, is by finding some points on the graph and then connecting them.
To find the points we need to evaluate the quadratic equation.
if x = 0
y = 5*0^2 + 2 = 2
So we have the point (0, 2)
if x = 1
y = 5*1^2 + 2 = 7
So we have the point (1, 7)
if x = -1
y = 5*(-1)^2 + 2 = 7
So we have the point (-1, 7)
And so on, once you have enough points, you can graph them on the coordinate axis and then connect them. The graph of the quadratic equation can be seen on the image at the end.
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Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20 years. Also, find the APY for the account. A $1000 deposit in an account with an APR of 3%. The balance in the account after 1 year is approximately
The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
What is meant by continuous compounding?
If compound interest is calculated and reinvested into the balance of an account across an essentially unlimited number of periods, continuous compounding is the mathematical limit that compound interest can reach. Continuous compounding determines interest by assuming constant compounding across an infinite number of periods, as opposed to computing interest on a finite number of periods, such as annually or monthly.
Given,
rate per period = 3%
Principal amount = $1000
Compounding is done after 1,5 and 20 years.
But we are asked to find the amount after continuous compounding after 1 year.
The formula of the amount after continuous compounding is:
[tex]A = Pe^{rt}[/tex]
where A = amount after continuous compounding
r = rate of period
t = time period
P = principal amount
[tex]A = Pe^{rt} = 1000e^{0.03*1}[/tex] = $1030.45
Annual yield formula (AYP) = [tex](1+\frac{r}{n} )^n-1[/tex]
n = times it compounds per year = 365
r = 0.03
AYP = [tex](1+\frac{0.03}{365} )^{365}-1 = 0.0304[/tex]
= 3.04%
Therefore The balance in the account after 1 year due to continuous compounding is approximately $1030.45 and AYP is 3.04%.
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At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain.How many cups of iced tea did people drink during the party?
Answer:
3,641 cups drank
Step-by-step explanation:
A quart is 4 cups
At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups
At the end of the party, only 7 cups remained
3648 - 7 = 3,641 cups drank
rewrite the equation in vertex form. y^2-4y-x+9=0
In the vertex form the equation can be rewritten as x = 1×(y - 2)² + 5
The equation is given in the standard form y²-4y-x+9 = 0 and we have to convert it into vertex form
So basically, the general vertex form of any equation is x = a(y - k)² + h
⇒ y²-4y-x+9 = 0
Shifting the x to RHS,
⇒ x = y²- 4y + 9
Writing y²- 4y in the form of (a-b)²,
⇒ x = y²- 4y + 4 + 5
⇒ x = 1×(y - 2)² + 5,
Hence the equation is now converted to vertex form
⇒ where a = 1, k = 2 and h = 5
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Frank borrowed $200 from his parents to buy a mountain bike. Each week, he uses $14 of his allowance to pay back his parents. Let x represent the number of weeks that have passed since he borrowed the money and let y represent the amount of money Frank still owes.
a. Why is $200 the y-intercept in this situation?
b. Write a linear equation for this situation.
c. Create a graph that shows the amount Frank still owes his
parents through the first five weeks.
d. How much will Frank’s last payment be?
Answer:
Step-by-step explanation:
200-14=186
Frank still needs to give 186
what is y:x if 4x-6y=7x+2y
Please Answer Quick!
Answer:
x = 5/2
y = 1/2
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 6y = 7x + 2y[/tex]
[tex]\qquad \sf \dashrightarrow \: 4x - 7x = 2y + 6y[/tex]
[tex]\qquad \sf \dashrightarrow \: 8y = - 3x[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - \dfrac{3}{8} x[/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{y}{x} = - \dfrac{3}{8} [/tex]
[tex]\qquad \sf \dashrightarrow \: {y}:{x} = - {3}:{8} [/tex]
That's our required ratio ~
Population increase in India India had one billion people in 2001. Its growth rate was 1.8% per year. By how many people did the population increase the first year?
The population increased by 18 million at the end of one year at the rate of 1.8%.
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. Alternatively put, it is the relationship between a component and a whole in which the value of "whole" is always assumed to be 100.
For instance, if a student receives 15 out of 50 in math, one can determine the relevant percentage by expressing "marks earned" as a fraction of "total marks" and multiplying the result by 100. i.e., the percentage of marks is equal to 15 / 50 100, or 30%.
Given that, population of India is one billion.
The rate of increase is 1.8%.
After one year the population will be:
P = (1000000000)(1.8/100)
P = 18000000
Hence, the population increased by 18 million at the end of one year at the rate of 1.8%.
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Solve for x with the given measures
The measure of angle the value of x =-96.
What is parallelogram?
A parallelogram is a special kind of quadrilateral composed of parallel lines. Any angle between the adjacent sides of a parallelogram is allowed as long as the opposite sides are parallel. A quadrilateral is a parallelogram if its two opposite sides are parallel and congruent. A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel and equal.
With the use of alternate interior angles, we can quickly resolve this. Right, the interior of a parallelogram is always 360 degrees.
(-x-6)° = 90
x = -96
Hence The measure of angle the value of x =-96.
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