Using proportions, it is found that the possible amounts that he will spend on candy are represented by the inequality [tex]c \leq 54[/tex].
What is a proportion?A proportion is a fraction of a total amount.
In this problem, each pound of candy costs $6, and he will buy at most 9 pounds, hence the maximum amount he will spend is given by:
M = $6 x 9 = $54.
Hence, the possible amounts that he will spend on candy are represented by the inequality [tex]c \leq 54[/tex].
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Angelina’s family owns a mini-golf course. When discussing the business with a customer, she explains there is a relationship between the number of visitors and hole-in-one winners. If x is the number of visitors and y is the number of winners, which conclusion is correct?
The ordered pair (–3, 7) is viable.
The ordered pair (0, 4) is viable.
The ordered pair (7, 0) is non-viable.
The ordered pair (12, 3) is viable.
Answer:
D
Step-by-step explanation:
X must be positive as you cannot have a negative amount of people and neither X and Y could be 0. (In this case (7, 0) could have been viable but the choice says non-viable.) This means the answer is (12,3).
The ordered pair (12, 3) is viable is correct answer.
What is ordered pair?"Ordered pair is defined as the two numbers or variables which is written in form of pair using parenthesis."
According to the question,
Number of visitors = x
Number of winners = y
Relationship given,
Number of visitors and hole in one winners.
Negative value cannot be part of number of visitors or winners.
Therefore,
(-3,7) is not the correct ordered pair.
'x' and 'y' value cannot be equals to zero as per the condition given.
(7,0) is non viable.
Therefore,
(0,4) and (7,0) is not the correct ordered pair.
(12,3) represent both positive value as per the condition.
Hence, the ordered pair (12, 3) is viable is correct answer.
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HELP PLEASE FOR NUMER 3 and 4 PLEAESE ASAP ANI WILL GIVE BRANILESS FOR THE FIRST PERSON
Wheres the ? n answers at for #3 n #4
The camp has two fire pits. One is a rectangular fire pit with a perimeter of 20 inches. The
other is a circular fire pit with a circumference of 7 inches. Shakir will place stones along
the outside edges of both fire pits. If each stone is the same size, which pit will require more
stones? Use the space below for your work. Explain how you know.
Please help!!
18x3 + 6x2y - 9x2 - 3xy
factor completely
Answer:
[tex]\sf 3x(3x+y)(2x-1)[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf 18x^3 + 6x^2y - 9x^2 - 3xy[/tex]
Factor out common term [tex]\sf 3x[/tex]:
[tex]\sf \implies 3x(6x^2 + 2xy - 3x - y)[/tex]
Factor [tex]\sf (6x^2 + 2xy - 3x - y)[/tex]
Rearrange:
[tex]\sf \implies 6x^2 - 3x+ 2xy - y[/tex]
Factor pairs of terms:
[tex]\sf \implies 3x(2x-1)+ y(2x - 1)[/tex]
Factor out common term (2x - 1):
[tex]\sf \implies (3x+y)(2x-1)[/tex]
Final solution:
[tex]\sf \implies 3x(3x+y)(2x-1)[/tex]
Answer:
6x2y(3xy2 − 1)
Step-by-step explanation:
i got it right on my quiz :D
it is 3 kilometers from Linda's house to the nearest mailbox. How far is it in meters? Be sure to include the correct unit in your answer.
Answer:
1km=1000m... thats basically the answer so the nearest mail box is 3000M
Help fast please and thank you!
Answer: 1/4 .!
Step-by-step explanation: hope this helped :).
Which expression is equivalent to (q^6)^2
○ q^3
○ q^8
○ q^12
○ q^36
btw, its not q^36
Rounding please help! Math
it is just still 5 I believe :P hope this helps
A principal of a large high school wants to estimate the true proportion of high school students who use the community's public library. To do so, he selects a random sample of 50 students and asks them if they use the community's public library. The 95% confidence interval for the true proportion of all students who use the community's public library is 0.25 to 0.34. If the principal had used a sample size of 200 students rather than 50 students, how would the length of the second interval compare to the original interval?
O It would be half as wide.
O It would be twice as wide.
O It would be one-fourth as wide.
O It would be four times as wide
ws
Considering the margin of error of a confidence interval, it is found that the correct option is:
It would be half as wide.
What is the margin of error of a confidence interval?It is modeled by:
[tex]M = z\frac{s}{\sqrt{n}}[/tex]
In which:
z is the critical value.s is the standard deviation.n is the sample size.From this, we get that the margin of error is inversely proportional to the square root of the sample size. Then, multiplying the sample size by 4, when it changes from 50 to 200, cuts the margin of error in half, making the interval half as wide.
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Answer: It would be half as wide
Step-by-step explanation:
If the principal had used a sample size of 200 students rather than 50 students, the length of the second interval would be half as wide compared to the original interval.
The width of a confidence interval is inversely proportional to the square root of the sample size. In this case, the sample size is multiplied by 4 (from 50 to 200), so the square root of the sample size is doubled. As a result, the width of the confidence interval is divided by 2, making it half as wide.
Therefore, the correct answer is: It would be half as wide.
Bo needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged him $63 for parts. The total was $551.75. What was the cost of labor, per hour?
The area of a circle is 36π cm². What is the circumference, in centimeters? Express your answer in terms of π
Answer: [tex]12\pi[/tex]
Step-by-step explanation:
The formula for area of a circle is [tex]\pi r^2=A[/tex]
The formula for circumference of a circle is [tex]2r\pi=C[/tex]
Where r is the radius
A is area
C is circumference
Knowing this we can sub our values in and solve for r in the formula for area
Divide both sides by [tex]\pi[/tex] to isolate r
[tex]\pi r^2=A\\\pi r^2=36\pi \\\frac{\pi r^2}{\pi } =\frac{36\pi }{\pi } \\r^2=36[/tex]
Take the square root of both sides
[tex]r^2=36\\\sqrt{r^2} =\sqrt{36} \\r=6[/tex]
Now sub the value of r into the formula for circumference
[tex]2r\pi =C\\2(6)\pi =C\\12\pi[/tex]
Answer:
[tex]12\pi \: c \: m[/tex]
step by step explanation:
[tex]area \: of \: a \: cirle = \pi \: r {}^{2} \\ circmferene \: of \: a \: circle = 2 \:\pi \: r \\ 36\pi = \pi \: r {}^{2} \\ 36 = r {}^{2} \\ r = 6 \\ for \: circmference \\ 2 \times \pi \: \times 6 = 12\ \: \pi \: cm [/tex]
A figure is made up of three triangles. Each triangle has a base of 5 feet and a height of 4.5 feet. What is the total area of the figure?
Group of answer choices
33.75 ft²
43.75 ft²
67.5 ft²
22.5 ft²
Answer:
Step-by-step explanation:
3 * 1/2 * 5 * 4.5
= 33.75 fT^2.
Really need help, I’m trying to catch up in my math and get my marks back up before mid term..
Answer:
a) 12x + 22 b) 17[tex]x^{2}[/tex] - x
Step-by-step explanation:
Perimeter is the sum of the each side length.
The first example is a rectangle so the (4x+8) and the (2x+3) are doubled.
(4x+8) x 2 = 8x+16
(2x+3) x 2 = 4x + 6
12x+22
(6[tex]x^{2}[/tex] - 12x) + (2[tex]x^{2}[/tex] + x) + (9[tex]x^{2}[/tex] + 10x)
combine like-terms.
17[tex]x^{2}[/tex] - x
Answer:
12x + 22 for the rectangle, 17x^2 - x for the triangle
Step-by-step explanation:
The perimeter of a square/rectangle is equal to 2*width + 2*length
So for the rectangle, it would be 2*(4x + 8) + 2*(2x + 3)
This can be further simplified as 8x + 16 + 4x + 6
Which can be further simplified as 12x + 22
The perimeter of a triangle is equal to length if side one + length of side two + length of base
That would be (6x^2 - 12x) + (2x^2 + x) + (9x^2 + 10x)
Which becomes 8x^2 - 11x + (9x^2 + 10x)
17x^2 - x
3
14) There are seven million, eight hundred and fifty-four thousand,
three hundred and eight people in a country. i lleda
Round this number to the nearest ten thousand people.
Answer:
7,854,000
because the 308 people would have to be at least 500 to round up to 7,855,000
What is the median age of a group of employees
whose ages are 32, 37, 30, 43, 29 and 31?
If ∠GHJ≅∠IHJ and GJ=99, what is IJ?
Answer:
99
Step-by-step explanation:
Triangles GJH and IJH are congruent, so GJ=IJ=99.
compute (5 2/3)^2-(4 1/3)^2
Answer:
40/3
Step-by-step explanation: If you have a calculator type in (5 2/3)^2-(4 1/3)^2. To get 40/3. So in short, square (5 2/3)^2 to get 289/9 and square (4 1/3)^2 to get 169/9. Then subtract the two 289/9-169/9 to get 40/3.
Erin wants to fill the jewelry box with beads. One package of beads is 120 cubic inches. How many packages of beads should Erin purchase to fill the jewelry box completely?
Answer:
9 packages of beads
Step-by-step explanation:
volume of cuboid = area of base × height
⇒ volume of jewelry box = (15 × 12) × 6
= 180 × 6
= 1080 in³
Given:
1 package of beads = 120 in³Number of packages of beads = volume of box ÷ volume of 1 package of beads
⇒ Number of packages of beads = 1080 ÷ 120
= 9
Which ordered pair would form a proportional relationship with the point graphed below?
(–40, 20)
(–10, –20)
(15, –30)
(5, –15)
Answer:
(c) (15, -30)
Step-by-step explanation:
A proportional relationship has the equation ...
y = kx
The value of the constant of proportionality is the ratio of y to x:
k = y/x = 40/-20 = -2
__
The point that is on the line y = -2x is the point (15, -30).
What is the volume of a sphere with a diameter of 7.5 cm, rounded to the nearest tenth of a cubic centimeter?
Answer:
V≈220.89cm³
Step-by-step explanation:
Answer: 220.9
4/3 π(3.75)^3=220.9
For each of the figures, write an absoulute value equation that has the following solution set.
The solution set -18 and 0 are the true values of the absolute value equation
The absolute value equation that has the a solution set of -18 and 0 is |x + 9| = 9
How to determine the absolute value equation?From the figure, the solution sets of the absolute value equation are given as:
x = {-18, 0}
Calculate the mean of the solution set
Mean = 0.5 * (-18 + 0)
Mean = -9
Calculate the difference of the solution set divided by 2
Difference = (0 + 18)/2
Difference = 9
The absolute value equation is the represented as:
|x - Mean| = Difference
Substitute known values
|x + 9| = 9
Hence, the absolute value equation that has the a solution set of -18 and 0 is |x + 9| = 9
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Answer:
|x+9|=9
Step-by-step explanation:
How do you do this problem:
1- 3 (4 - 3) + (27- 2 x 3)
Answer:
19
Step-by-step explanation:
Do what is in parenthesis first.
(4 - 3) = 1
(27 - 2 * 3) = (27 - 6) = 21
Now the equation looks like this:
1 - 3 (1) + (21) =
1 - 3 + 21 =
19
U is the midpoint of TV and S is the midpoint of RT.
If RV=w and SU=w–30, what is RV?
Answer:
60
Step-by-step explanation:
By the triangle midsegment theorem, 2(SU)=RV.
2(w-30)=w, meaning w=60.
So, RV=60 as well
What are the new coordinates of the figure above if it is rotated 90 degrees clockwise about the origin ?
A. A’(1,-3), B’(1,-7),C’(-3,-7),D’(-3,-3)
B. A’(-3,-1),B’(-7,-1), C’(-7,3) D’(-3,3)
C. A’(-3,-1),B’(-7,-1),C’(-7,3),D(-3,3)
D.A’ (1,-3),B’(1,-7),C’(3,-7),D’(3,-3)
Answer: A
Step-by-step explanation:
If v is the circumcenter of pqr ,pr =46 ,tv=15,and vr=25 find each measure
Answer:
1. a) SR = 23
b) QV = 25
c) QT = 20
d) PQ = 40
e) VS = 4·√6
2. a) LH = 16
b) EL = 2·√185
c) JG = 30
d) EK = 22
e) KG = 30
3. a) XT = 37
b) TZ = 34
c) ZW = 17
d) XZ = 21
e) SY = 69
Step-by-step explanation:
The circumcenter ΔPQR is the center of the circle that circumscribes ΔPQR
The length of the radius of the circle ≡ VR = VP = QV = 25
a) Given that VR ≅ VP - Radius of circumcircle
VS ≅ VS Reflective property
∠VPS ≅ ∠VRS - Base angles of an isosceles triangle
Right triangle VPS ≅ Right triangle VRS -Hypotenuse and one Leg HL congruency
Therefore, SR ≅ PS -Corresponding parts of congruent triangles are congruent CPCTC
SR + PS = PR = 46
SR + PS = SR + SR = 2·SR = 46
∴ SR = 46/2 = 23
b) QV = VR = 25 = Radius of circumcircle of ΔPQR -Given V = center and Q = vertices of the triangle circumscribed by the circle referred to in the question
c) QT = √(QV² - TV²) = √(25² - 15²) = √400 = 20
d) TV ≅ TV - Reflexive property of congruency
ΔTQV ≅ ΔTVP - Hypotenuse and one Leg (HL) congruency
QT ≅ TP -Corresponding parts of congruent triangles are congruent CPCTC
PQ = QT + TP Given
∴ PQ = QT + QT since QT = TP
PQ = 2·QT = 2 × 20 = 40
e) VS = √(VR² - SR²) = √(25² - 23²) = √96 = 4·√6
2. The incenter is the center of the incircle of ΔEFG
a) LH = LK = JL = 16 -Radius of incircle of ΔEFG
b) EL = Hypotenuse of right triangle LHE = √(LH² + EH²) = √(16² + 22²) = √740 = 2·√185
c) JG = Leg length of right triangle JGL = √(LG² - JL²) = √(34² - 16²) = √900 = 30
d) EK = Leg length of right triangle LKE = √(EL² - LK²) = √(740 - 256) = 22
e) KG = Leg length of right triangle LKG = √(LG² - LK²) = √(34²- 16²) = √900 = 30
3. Point Z id the centroid of ΔRST
a) XT = XS - point X on ST bisected by median line RX
ST = XT + XS = XT + XT = 2.XT = 74
XT = 74/2 = 37
b) TZ = 2/3×TW - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
TZ = 2/3×51 = 34
c) TZ + ZW = TW
∴ ZW = TW - TZ = 51 - 34 = 17
d) RZ = 42 = 2/3×RX - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
∴ RX = 3/2×42 = 63
RZ + XZ = RX - Given
XZ = RX - RZ = 63 - 42 = 21
e) SZ = 2/3×SY - Length from a vertex to the centroid on a median line is equal to two third the length of the median line
SZ + ZY = SY
∴ ZY = SY - SZ = SY - 2/3×SY = 1/3×SY = 23
Which gives;
SY = 3 × 23 = 69.
Eva loves to go fishing. Each time she catches a fish, there is a 70% chance that it is a northern pike and a 30%
chance it is a walleye. Let W be the random variable that represents the number of walleye Eva gets if she
catches 2 fish.
W = # of walleye 0
1
2
P(W)
0. 49
0. 42
0. 09
Calculate the mean of W.
walleye
Uw =
Answer:
Answer: 1.4
Step-by-step explanation:
P(Northern pike) = 0.7
P(walleye) = 0.3
If 2 fishes are caught :
Number of northern pike (x) :
X = 0
P(walleye 1 st) * p(walleye 2nd) = (0.3 * 0.3) = 0.09
X = 1
P(walleye 1st)*P(Northern pike 2nd) OR P(Northern pike 1st)*P(Walleye 2nd)
= (0.3 * 0.7) + (0.7 * 0.3)
= 0.21 + 0.21
= 0.42
P(x = 2)
P(northern pike 1st) * P(northen pike 2nd)
0.7 *0.7 = 0.49
X: _ 0 _ 1 __ 2
P(x): ___ 0.09 ___ 0.42 ____ 0.49
Expected value of northern pikes :
(0* 0.09) + (1 * 0.42) + (2 * 0.49)
0 + 0.42 + 0.98
= 1.4
Expected value of the number of walleye is 0.5.
What is the expected value?
The expected value exists as a long-run average value of random variables. It also demonstrates the probability-weighted average of all possible values. Expected value exists as a generally utilized financial concept.
W = # of walleye 0, 1, 2
P(W) 0. 49, 0. 42, 0. 09
To estimate the expected value of the number of walleye.
E(X) = number of walleye
E(X) = (0 [tex]\times[/tex] 0.49) + (1 [tex]\times[/tex] 0.42) + (2 [tex]\times[/tex] 0.09)
E(X) = 0 + 0.42 + 0.08
E(X) = 0.5
Therefore, the number of walleye expected value = 0.5.
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Are the base angles of an isosceles triangle always congruent?
Answer: Yes
Step-by-step explanation:
If you draw the altitude of an isosceles triangle from the vertex angle, then the two triangles formed are congruent, meaning the base angles are congruent by CPCTC.
Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
What is the isosceles triangle?An isosceles triangle is a triangle that has at least two sides of equal length.
When an altitude is drawn to the base of the isosceles triangle, it bisects the vertex angle. As it bisects the base, the two congruent triangles are created.
An isosceles triangle with only two congruent sides, the congruent sides are called legs. The third side is called the base. The angle opposite the base is called the vertex angle, and the angles opposite the legs are called base angles.Hence, Yes, the base angles of an isosceles triangle are congruent because in n isosceles triangle two of its sides are always congruent, and also angles opposite to congruent sides are congruent.
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SYSTEM OF EQUATIONS- I struggle with this
Person A wants to order a bunch of shirts. One website charges 9.65 per shirt, plus a set up fee for $43. Another company charges 8.40 per shirt plus a $58 fee. But what number of shirts would the cost be the same? Why?
Answer:
12 shirts
Step-by-step explanation:
First, we need to write our equations. Let x be the number of shirts and y be the cost. We will multiply the number of shirts bought (x) by the price and then add the setup fee.
To answer the overall question, we will graph the two equations we create. Their point of intersection is the solution, or where the number of shirts bought would cost the same.
"One website" - 9.65 per shirt, plus a set up fee for $43
y = 9.65x + $43
"Another company" - 8.40 per shirt plus a $58 fee
y = 8.4x + $58
See attached for the graph.
They intersect at point (12, 158.8) meaning that both websites will charge $158.80 for 12 shirts.
50 POINTS 50 POINTS please help me with these 5 questions attached pictures
Step-by-step explanation:
the first graph
0=|x+2| f(0)=|0+2|
|x+2|=0 f(0)=|2|
x+2=0 f(0)=2
x=-2
Answer:
First graph X=-2
simplified?
0.0007 - (4.9 × 10^-7)
A.
4.8993 × 1^0-7
B.
6.9951 × 10^-7
C.
2.1 × 10^-4
D.
6.9951 × 10^-4
Answer:
Option B
Step-by-step explanation:
Given the following question:
In order to find the answer, we need to convert the scientific notation into standard notation and then simplify by subtracting the decimals. Then we convert the standard notation back into scientific notation.
[tex]0.0007 - (4.9\times 10^{-7} )[/tex]
[tex]4.9\times10^{-7} =0.00000049[/tex]
[tex]0.0007-0.00000049[/tex]
[tex]0.0007-0.00000049=0.00069951[/tex]
[tex]=0.00069951[/tex]
[tex]0.00069951=6.9951 \times10^{-7}[/tex]
[tex]=6.9951 \times10^{-7}[/tex]
Your answer is "6.9951 × 10^-7" or option B.
Hope this helps.