The expression 6y² - 48 + 42y is factored by first rearranging the terms, finding the GCF, and then factoring the resulting trinomial to get 6(y + 8)(y - 1).
To factor the expression 6y² - 48 + 42y, the first step is to rearrange the terms in descending powers of y, which gives us 6y² + 42y - 48. Next, we can look for a greatest common factor (GCF) among the three terms. Observing that each term is divisible by 6, we can factor out 6:
6(y² + 7y - 8)
Now, we need to factor the trinomial within the parentheses. We are looking for two numbers that multiply to give -8 (coefficient of y² times constant term), and add to 7 (coefficient of y term). The numbers +8 and -1 satisfy these conditions:
6(y + 8)(y - 1)
Thus, the original expression 6y² - 48 + 42y factors to 6(y + 8)(y - 1).
Mr. Clark claims that he has a coin that is weighted so that the probability of heads is 40%. To test this, his students flip the coin 200 times and calculate the relative frequency of heads and tails.
Outcome Heads Tails
Relative frequency 0.38 0.62
Select from the drop-down menus to correctly complete each statement.
The relative frequency of heads is
40%.
Mr. Clark's claim about the theoretical probability is likely to be
.
This means that the theoretical probability of tails is most likely
for this coin.
how many books can you get in a storage bin that is 4 feet high and 9 feet long and 11 feet wide
What is the geometric mean of 6 and 13?
What is the Geometric mean a 5 and 45?
Answer: [tex]\sqrt{78}[/tex] and [tex]15[/tex]
Step-by-step explanation:
Given: (1) two numbers [tex]6[/tex] and [tex]13[/tex].
(2) two numbers [tex]5[/tex] and [tex]45[/tex].
To Find: Geometric number of numbers in [tex](1)[/tex] and [tex](2)[/tex]
Solution:
Let first number be [tex]=\text{a}[/tex]
Let second number be [tex]=\text{b}[/tex]
Geometric mean of two numbers [tex]\text{a}[/tex] and [tex]\text{b}[/tex] is
[tex]\sqrt{\text{a}\text{b}}[/tex]
Now,
[tex](1)[/tex] First number is [tex]=6[/tex]
Second number is [tex]=13[/tex]
Geometric mean of both numbers is
[tex]\sqrt{6\times13}[/tex]
[tex]\sqrt{78}[/tex]
Geometric mean is [tex]\sqrt{78}[/tex]
[tex](2)[/tex] First number is [tex]=5[/tex]
Second number is [tex]=45[/tex]
Geometric mean of both numbers is
[tex]\sqrt{5\times45}[/tex]
[tex]\sqrt{225}[/tex]
[tex]15[/tex]
Geometric mean is [tex]15[/tex]
Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. a pollster contacts 92 people in the 18-21 age bracket and finds that 78 of them respond and 14 refuse to respond. when 284 people in the 22-29 age bracket are contacted, 265 respond and 19 refuse to respond. assume that 1 of the 376 people is randomly selected. find the probability of getting someone in the 22-29 age bracket or someone who refused to respond.
Final answer:
The probability of selecting a person from the 22-29 age bracket or someone who refused to respond is approximately 79.3% out of the total number of people contacted.
Explanation:
The student is asking about finding the probability of selecting either a person from the 22-29 age bracket or someone who refused to respond from a combined group of people contacted in a survey. To solve this problem, we use the addition rule of probability. The total number of people is 376. The number of people who are in the 22-29 age bracket is 284, and the number of people who refused to respond is 14+19=33. However, this would include those who refused from the 22-29 bracket twice, so we subtract the 19 from the 22-29 age group who refused, leaving us with 33-19=14. Thus, the total number in either category is the sum of these, 284+14=298.
The probability (P) of picking someone from the 22-29 age bracket or someone who refused to respond is therefore calculated as:
P = Number in either category / Total number = 298 / 376 ≈ 0.793 or 79.3%
A trapezoid has an area of 15 square feet. If the bases are 4 feet and 6 feet , what is the height of the trapezoid? Hurry Big test tomorrow this the last one
Final answer:
The height of the trapezoid is 3 feet.
Explanation:
To find the height of a trapezoid with given bases and area, you can use the formula for the area of a trapezoid, which is the average of the two bases multiplied by the height. The formula is as follows:
Area = ½ × (base1 + base2) × height
Given that the area of the trapezoid is 15 square feet and the two bases are 4 feet and 6 feet, the formula becomes:
15 = ½ × (4 + 6) × height
This simplifies to:
15 = ½ × 10 × height
Therefore, we can calculate the height by dividing the area by 5 (which is half of 10):
height = 15 ÷ 5 = 3 feet
So, the height of the trapezoid is 3 feet.
the segments shown below could form a triangle ac=9. cb=8. ba=17
No, the triangle can not form.
What is Triangle inequality?The sum of any two sides of a triangle is greater than the third side.
Given:
ac=9. cb=8. ba=17
The question is attached below.
We know each triangle satisfy the triangle inequality which state that the sum of the two shorter sides must exceed the length of the third side.
But ,9+8=17 which equal to the third side .
So, these segments do not form a triangle.
Learn more about triangle inequality here:
https://brainly.com/question/1163433
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given the equation W=CE2/2, solve for C
Answer:
[tex]C=\frac{2W}{E^2}[/tex]
Step-by-step explanation:
[tex]W=\frac{CE^2}{2}[/tex]
Solve for C
To solve for C, we need to get C alone
LEts start with eliminating 2 from the denominator
Multiply the equation by 2 on both sides
[tex]2W= CE^2[/tex]
To isolate C, divide both sides by E^2
[tex]\frac{2W}{E^2} =C[/tex]
[tex]C=\frac{2W}{E^2}[/tex]
“Find the equation of the line passing through (8,-2) & (7,-4). Write your equation in point-slope AND slope intercept forms.
Point slope form using (8,-2) _____
Point slope form using (7,-4) _____
Slope intercept form: y=2x-18
One drawer in a dresser contains 7 blue socks and 7 white socks. a second drawer contains 5 blue socks and 1 white socks. one sock is chosen from each drawer. what is the probability that they match? express the answer in decimals.
A quality control engineer tests the quality of produced computers. suppose that 5% of computers have defects, and defects occur independently of each other.
a. what is the expected number of defective computers in a shipment of twenty? 1
b. find the probability of exactly 3 defective computers in a shipment of twenty.
What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid? A.7.81 units B.3.61 units C.2.23 units D.3.32 units
Answer:
3.61
Step-by-step explanation:
Jerome went on a hike. He climbed three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour?
Final answer:
Jerome's hiking speed was calculated by dividing the distance he hiked, three-fourths of a mile, by the time it took him, two-thirds of an hour. This yielded a hiking speed of 1.125 miles per hour.
Explanation:
To calculate Jerome's hiking speed in miles per hour, we need to divide the distance he hiked by the time it took him. Jerome hiked three-fourths of a mile in two-thirds of an hour. To find the speed, we use the formula:
Speed = Distance ÷ Time
Speed = ¾ mile ÷ ⅓ hour
To divide fractions, we multiply by the reciprocal of the denominator:
Speed = ¾ × ⅔ = 3/4 × 3/2 = 9/8
This fraction simplifies to 1⅛ (1.125) miles per hour. So, Jerome's hiking speed was 1.125 miles per hour.
It is important to remember that when we talk about speed, we are referring to the distance traveled over a certain period of time regardless of the direction of travel.
When 2/3 of a number is added to 10 the result is 5 more than the number find the number g?
[tex]g-the\ number\\\\\dfrac{2}{3}g+10=g+5\qquad\text{multiply both sides by 3}\\\\2g+30=3g+15\qquad\text{subtract 30 from both sides}\\\\2g=3g-15\qquad\text{subtract 3g from both sides}\\\\-g=-15\qquad\text{change the signs}\\\\\boxed{g=15}[/tex]
61/100in word form,decimal
In the number 35.3816, the underlined three is __________ the other three.
suppose that a pair of 7 sided dice is tossed. What is the expected value of the sum?
The expected value of the sum when rolling a pair of 7-sided dice is 8.
Explanation:When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.
The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).
To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:
Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8
Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.
A box has dimensions of 3 inches, 5 inches and 7 inches what is the surface area
Final answer:
The surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is calculated using the formula 2lw + 2lh + 2wh, resulting in a total surface area of 142 square inches.
Explanation:
To calculate the surface area of a box with dimensions of 3 inches, 5 inches, and 7 inches, you would use the surface area formula for a rectangular prism. The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the prism.
In this case:
Length (l) = 3 inches
Width (w) = 5 inches
Height (h) = 7 inches
Now, plug these dimensions into the formula:
Surface Area = 2(3 inches × 5 inches) + 2(3 inches × 7 inches) + 2(5 inches × 7 inches)
Surface Area = 2(15) + 2(21) + 2(35)
Surface Area = 30 + 42 + 70
Surface Area = 142 square inches
Therefore, the surface area of a box with dimensions of 3 inches by 5 inches by 7 inches is 142 square inches.
Julia is an intern at an architecture firm. She is given an assignment to create a bell-shaped structure that is symmetrical. She writes the function f(x)=3 squareroot -|x-2|+6 to model the structure. Find the piecewise function that matches this absolute value function. Then, graph the function using a graphing calculator and describe what you see.
Answer:
The given function is
f(x)= 3 [tex]\sqrt\left- |x \right-2 |+6[/tex] ⇒[Absolute value function]
F(x)= 1. 3[tex]\sqrt {-(x-2)+6}[/tex] =[tex]3\sqrt {-x+2+6}=3\sqrt{-x+8}[/tex] when (x-2≥0→x≥2) ⇒[ Piecewise function]
2. [tex]3\sqrt{-[-(x-2)]+6}=3\sqrt{x-2+6}=3\sqrt{x+4}[/tex] when [ x-2<0→x<2]⇒[ Piecewise function]
We see there is a shape which is is in the form of dome,point of intersection of two curves being (2,7.348), symmetrical on both side of line x=2.
Dominic picks oranges from 18 trees. He picks 11.4 pounds of oranges from each tree. How many total pounds does Dominic pick?
If the cubic function P(x) includes the points (−4, 0), (0, 0), and (2, 0), which of the following represents this function?
The function cannot be determined with the given information.
Explanation:The given points (-4, 0), (0, 0), and (2, 0) indicate that the function is a cubic function with three real roots. A cubic function is of the form P(x) = ax^3 + bx^2 + cx + d. Since the function passes through the x-axis at (-4, 0), (0, 0), and (2, 0), the roots of the cubic function are -4, 0, and 2. Therefore, the function can be written as P(x) = a(x + 4)(x - 0)(x - 2). However, since a cubic function with three real roots has an odd degree, the coefficient 'a' must be negative or positive. This means that the function can also be written as P(x) = -a(x + 4)(x - 0)(x - 2) or P(x) = a(x + 4)(x - 0)(x - 2). So, the correct representation of the function cannot be determined with the given information.
subtracting/adding mixed fractions
What is the simplified form of the expression? x8 2y10 5x5
You owe $976.34 on a credit card that has an interest rate of 10.75% APR. You pay $100.00 at the end of each month.
You place the $100.00 in a savings account that earns a 2.75% APR. What is the difference in interest between savings earned and credit card interest paid
answer: $8.52
help!!!
All rectangles can also be classified as which of the following? Select all that apply. r
rhombus
square
parallelogram
trapezoid
quadrilateral
Answer:
All rectangles can also be classified as which of the following? Select all that apply. r
rhombus
square
parallelogram
trapezoid
quadrilateral
Step-by-step explanation:
In plane geometry, a rectangle is a parallelogram.
Parallelogram: its opposite sides are parallel, it can also be a square, or a rhombus.
In Euclidean geometry, a quadrilateral is a polygon that has four sides and four vertices.
The answer is: Rhombus, square, parallelogram, and quadrilateral.
Find direction numbers for the line of intersection of the planes x + y + z = 1 and x + z = 0. (enter your answers as a comma-separated list.)
Write the equation of the line passing through (−1, 0) and (0, −3).
The equation of the line passing through (-1, 0) and (0, -3) is y = -3x - 3, where -3 is the slope, and -3 is also the y-intercept.
The equation of a line can be written in slope-intercept form as y = mx + b, where m is the slope of the line, and b is the y-intercept. To find the slope m, we can use the two points given; the slope is the change in y over the change in x, which is (-3 - 0)/(0 - (-1)) = -3/1 = -3. With the slope found, and knowing that the line passes through the point (0, -3), we can say the y-intercept b is -3. The equation of the line through the points (-1, 0) and (0, -3) is y = -3x - 3.
what is r divided by 8
20 POINTS!!
a triangle has side lengths 20cm, 27cm, 21cm. is the triangle a right angle? show your work
Weight Gain after gaining 25 pounds, a person is 115 pounds lighter than double his previous weight. How much did the person weigh before gaining 25 pounds? How could I write this problem
3 sin2(θ) + 16 sin(θ) − 35 = 0