The binomials which correctly represent the factors of the given trinomial; x² + x - 30 as required in the task content are; ( x - 5 ) and ( x + 6 ).
Which binomials correctly represents the factors of the given trinomial?As evident in the task content; the given trinomial whose binomial factors are to be determined is; x² + x - 30.
By factorisation; the given trinomial expression can be written as;
x² + 6x - 5x - 30
x ( x + 6 ) -5 ( x + 6 )
( x - 5 ) ( x + 6 )
On this note, the required binomials which are factors of the given trinomial expression are; ( x - 5 ) and ( x + 6 ).
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find the inverse of the function
f (x) = 15 + sqrt 5x - 5
[tex]15 + \sqrt{5x - 5} = f(x)[/tex]
Replace y for x and vice versa
[tex]15 + \sqrt{5y - 5} = x[/tex]
Solve for y.
[tex]15 + 5y - 5 = {x}^{2} [/tex]
[tex]15 + 5y = {x}^{2} + 5[/tex]
[tex]5y = {x}^{2} - 10[/tex]
[tex]y = \frac{ {x}^{2} - 10 }{5} [/tex]
[tex]f {}^{ - 1} (x) = \frac{ {x}^{2} - 10 }{5} [/tex]
If
6. Which of the following is true about the line given by 8x - 2y = 24?
A) The slope is negative.
B) The y-intercept is negative.
C) The x-intercept is 8.
D) The line does not pass through quadrant III.
Answer:
B
Step-by-step explanation:
put equation in slope-intercept formula (y=mx+b)
8x-2y=24
-8x -8x
-2y=-8x+24
divide each side by -2
y=4x-12
the "b" in the formula is the y-intercept which is -12, therefore B is correct
The order of rotational symmetry of the given figure is
Question 7 options:
A)
7.
B)
5.
C)
6.
D)
8.
Answer:
A
Step-by-step explanation:
A machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long. What is the total length needed in inches?
The total length needed in inches will be 490.5 inches.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long The total length needed in inches will be:
= (3 ft 4 7/8 inch × 12)
Note that 1 feet = 12 inches
= (12 × 3) + (4 7/8) × 12
= (36 + 4.875) × 12
= 490.5 inches
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Need it ASAP, please!!!
Answer:
27y - 45 + 7z
what is the experimental probability of spinning a white or yellow?
PLEASE PLEASE PLEASE HURRY ITS DUE TOMORROW!!!!!!
yellow / 5
blue / 12
green / 8
white / 9
red / 6
The experimental probability of spinning a white or yellow is 7/20
How to determine the experimental probability of spinning a white or yellow?From the question, we have the following parameters that can be used in our computation:
Outcomes of experiments
The outcomes of experiments are given as
yellow / 5
blue / 12
green / 8
white / 9
red / 6
The experimental probability of spinning a white or yellow can be calculated using the following equation
P(White or Yellow) =P(White) + P(Yellow)
Substitute the known values in the above equation, so, we have the following representation
P(White or Yellow) = (9 + 5)/5 + 12 + 8 + 9 + 6)
Evaluate the sum
P(White or Yellow) = 14/40
Simplify
P(White or Yellow) = 7/20
Hence, the probability is 7/20
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A box has the shape of a rectangular prism with height 28 cm. If the
height is increased by 0.6 cm, by how much does the surface area of
the box increase?
28 στη
16 cm
3.4 cm
Use pencil and paper. Show your work. Then show a second way to
solve the problem. Explain which way you like better and why.
The surface area increases by cm2.
Answer:
23.16
Step-by-step explanation:
Bismah is building 5 raised garden beds in a community garden. Each raised
garden bed will need 1 7/8 bags of soil. How many bags of soil will Bismah need for
8
all 5 raised garden beds?
5 5/8bags of soil
9 3/8 bags of soil
9 5/8 bags of soil
8 7/8 bags of soil
5 3/8 bags of soil
The fraction of soil bags Will needs in total for all 5 raised garden beds is 9 3/8.
What is community?In mathematics, community is the study of how objects interact and relate to each other. It focuses on analyzing the relationships between elements and understanding how they interact to form each other. Also explore how changes in one element affect other elements. Community in mathematics is also about recognizing patterns, finding solutions, and exploring the impact of change. It is an integral part of mathematics and is used in many areas of study such as algebra, geometry, and calculus. This can be calculated by multiplying the number of raised beds (5) by the amount of soil required per raised bed.
(1 7/8 bag).
5 x 1 7/8
= 9 3/8 bags
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I’ve been stuck on this for about a week, I know it might seem easy but I’m very bad at fractions and my teacher won’t help me
On solving the provided question we can say that - the increased value in fraction will be [tex]3\frac{1}{4}[/tex]
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
we have,
initial = [tex]4\frac{5}{6}[/tex]
increased by = [tex]4\frac{1}{4}[/tex]
son difference is = [tex]3\frac{1}{4}[/tex]
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The table shows the types and numbers of prizes at a carnival game what is the ratio of stuffed animals to posters
Answer:
Step-by-step explanation:
3
Angelique has a bag that contains six red marbles and four blue marbles and 14 yellow marbles if she chooses one marble from the bag what is the probability that marble is not yellow
Answer:
33.3% that the marble is not yellow
Rachel has 13 books and some empty boxes. She can put 4 books in each box. How many boxes can she fill completely?
How many books will be left over?
Answer:
she can fill 3 boxes completely and one book will be left over
Step-by-step explanation:
if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over
Are x and y proportional when Y /X equals five
Answer:
no
Step-by-step explanation:
The ratio of men to women working for a company is 6 to 5 . If there are 105 women working for the company, what is the total number of employees?
Answer:
231 employees
Step-by-step explanation:
The ratio of men to women working for the company is 6 to 5, which means that for every 5 women working at the company, there are 6 men working at the company.
Since there are 105 women working at the company,
there are 6/5 * 105 = 126 men working at the company.
In total, there are 126 men + 105 women = 231 employees working for the company.
helppp mee nowww plssss
Answer:
the answer is D, Mars is one of the smallest planets
Please help me I don’t understand this at all
A, C, and D are the answers.
A certain retail store bases its staffing on the number of customers that arrive during certain time slots. Based on prior experience this store expects 32% of its customers between 8:00 am and 12:00 pm; 21% of its customers between 12:00 pm and 4:00 pm; 35% of its customers between 4:00 pm and 8:00 pm; and 12% of its customers between 8:00 pm and midnight. On a certain day, the store had 214, 198, 276, and 134 customers in those time slots, respectively. Should the store change its staffing? What was wrong with this solution?
Answer:
Step-by-step explanation:
Based on the data gathered on that certain day, I would say NO, the store does not need to change its staffing. The data shows that the percentages calculated by the store are extremely close to the actual percentage of people that arrived at those given hours throughout the day. The problem with this solution is that it does not take into account special circumstances, such as specific days, events, holidays, new popular items, etc. All of these can drastically affect the number of people that enter the store at a given time.
1. The retail store should not change its staffing arrangement.
2. Changing the staffing arrangement may not favor the retail store.
Data and Calculations:
8:00 am & 12:00 pm & 4:00 pm & 8:00 pm &
12:00 pm 4:00 pm 8:00 pm midnight
Expected % of customers 32% 21% 35% 12%
Actual number of customers 214 198 276 134
Total Number of customers = 822 (214 + 198 + 276 + 134)
Actual % of customers 26% 24% 34% 16%
Difference between expected percentage of
customers and actual 6% 3% 1% -4%
Variation 0.36% 0.09% 0.01% 0.16%
Sum of variation = 0.62%
Standard Deviation = 0.787
Thus, based on the standard deviation, the store should not change its staffing.
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Radius of a circle is 5 cm
Length of a rectangle is 9.2 cm
Width is 4 cm
Area of the shaded region is
A. 36.5 cm B. 41.7 cm2 C. 42.6 cm2
D. 48 cm2
Answer:
the answer is (b.)41.7cm²
the workings;;
9.2cm×4cm+5cm=41.8 or 41.7cm²
A marine biologist wants to test the effect of water temperature on the length of time sea otters can remain under water during a dive. He gathers data on randomly-selected dives by 7 different otters recording dive duration (in seconds) and water temperature (in degrees Celsius). A computer regression analysis of his data is given below. Assume all conditions for inference for slope have been met. Predictor Coef SE Coef Constant 52.789 5.257 10.04 0.000 Water temp 3.3684 0.4216 7.990 0.002 5.557 R-Sg 92.7% R-Sg (adj ) 91.3% = S =
Which of the following is the estimate of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship?
(a) 0.4216
(b) 0.4216
(c) 5.257
(d) 5.257
(e) 5.557
Which of the following is the best interpretation of the quantity S
(a) The sum of the squared deviations between each observed dive duration and the dive 2.
(b) The sum of the squared deviations between each observed water temperature and the
(c) The average distance between the water temperature for each dive and the mean water
(d) Predictions of dive duration from water temperature based on this regression model will
(e) The average distance between the duration of each dive and the mean dive duration for duration predicted by the regression equation is 5.557 seconds. water temperature predicted by the regression equation is 5.557 seconds. temperature for all the dives in this sample is about 5.557 seconds. be off by an average of about 5.557 seconds. all the dives in this sample is about 5.557 seconds.
Answer:
b
Step-by-step explanation:
The solution is : 0.4216 is the estimate of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
here, we have,
from the data given
The estimate of the standard deviation of the sampling distribution of b,
( The slope of the sample regression line for the relationship )
= 0.4216
i.e. intersection of SE coef and water temperature )
Testing the effect of water temperature on the length of time sea otters can remain
Hence, The solution is : 0.4216 is the estimate of the standard deviation of the sampling distribution of b, the slope of the sample regression line for this relationship.
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match the equation with its corresponding solution for x. 6= -1/3x+5
Answer:
x=-3
Step-by-step explanation:
find the area of the diagram below
Answer:
220
Step-by-step explanation:
formula for area of a triangle is 1/2 base times height in this case thats 1/2(10X6) which is 30 sense there are 4 multiply 30 by 4 to get 120 then add that to the area of a square which is 10X10 or a hundred to get 220
v + 9 over 3= 8
what is v?
Answer:
I love algebra anyways
the ans is in the picture with the steps
(hope it helps can i plz have brainlist :D hehe)
Step-by-step explanation:
If s is directly proportional to t, and s = 30 when t = 15, find t when s = 64.
Step-by-step explanation:
please refer to sketch for detail
Is this a right triangle? How do you know?
Answer:
Yes, Pythagorean theorem
Step-by-step explanation:
Yes, as by doing the Pythagorean theorem, a^2+b^2=c^2 you can confirm that it is.
8^2+15^2=17^2
64+225=17^2
289=17^2
(square root both sides)
17=17
Plz help me god blesss you
Answer:
d. III
Step-by-step explanation:
Quadrants:
In the first quadrant, both x and y are positive, that is, x > 0 and y > 0.
In the second quadrant, y is positive while x is negative, that is, x < 0 and y > 0.
In the third quadrant, both x and y are negative, that is, x < 0 and y < 0.
In the fourth quadrant, x is positive while y is negative, that is, x > 0 and y < 0.
In this question:
x < 0 and y < 0, so third quadrant, and the correct answer is given by option D.
What is the probability that (enter the probability only, do not round.):
• Exactly 2 are male?
• At least 7 are male?
• None are male?
• Less than 3 are male?
• There are 3 or 4 males?
• At least 1 is male?
Answer:
7
Step-by-step explanation:
The required probabilities are
• Exactly 2 are male = 0.08
• At least 7 are male = 0.14
• None are male = 0.60
• Less than 3 are male = 0.12
• There are 3 or 4 males = 0.019
• At least 1 is male = 0.04
Probabilities to college reported that 40% of its population is male. Nine students are selected at random.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
For Exactly 2 are male = 2 * 0.04
= 0.08
Similarly,
• At least 7 are male = 0.14
• None are male = 1 -0.40 = 0.60
• Less than 3 are male = 0.12
• There are 3 or 4 males = 0.12 *0.16 = 0.019
• At least 1 is male = 0.04
Thus, the required probability is given above.
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Mr. Paras sold a portion of his lot to his friend. The lot was 65 meters long and 32 meters
wide. However, part of it measuring 21 meters long and 3 meters wide was donated for
the right of way of his neighbors. What was the area of lot he sold excluding the right of
way?
1. What is the area of the lot that he supposed to sell?
2. What was the area of the donated lot for the right of way?
3. What was the area of the remaining lot that was actually sold?
Please answer it correctly huhu I really need it rn T - T
Answer:
1. What is the area of the lot that he supposed to sell?
65*32 = 2080 sq. m2. What was the area of the donated lot for the right of way?
21*3 = 63 sq. m3. What was the area of the remaining lot that was actually sold?
2080 - 63 = 2017 sq. mAnswer:
1.2,080 m²
2.63m²
3.2,017
4.25m²
5.81m²
Explanation:
1. A = LW
A = 65 m × 32 m
A = 2,080 m²
2. A = LW
A = 21 m × 3 m
A = 63m²
3. A = 2,080 m² – 63 m²
A = 2,017 m²
4. A = s²
A = (5m)²
A = 25 m²
5.
A = s²
A = (9 m)²
A = 81 m²
This is the right way or the wrong answer
Answer:
This is the right answer.
1. The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,290 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 153 of their customers and calculates that these customers used an average of 10,586kWh of electricity last year. Assuming that the population standard deviation is 2509kWh, is there sufficient evidence to support the power company's claim at the 0.05 level of significance? State the null and alternative hypotheses for the test.
2. The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,290 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 153 of their customers and calculates that these customers used an average of 10,446 kWh of electricity last year, Assuming that the population standard deviation is 2509 kWh, is there sufficient evidence to support the power company's claim at the 0.02 level of significance? Compute the value of the test statistic.
A. We reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the power company's claim that the mean amount of electricity for their residents is more than the national average.
B. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the power company claim that the mean amount of electricity for their residents is more than the national average.
C. We reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support the power company's claim that the mean amount of electricity for their residents is more than the national average.
D. We fail to reject the null hypothesis and conclude that there is sufficient evidence at a 0.02 level of significance to support the power company's claim that the mean amount of electricity for their residents is more than the national average.
Answer:
Kindly check explanation for (1)
2.)
B. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the power company claim that the mean amount of electricity for their residents is more than the national average.
Step-by-step explanation:
1.)
H0 : μ = 10290
H0 : μ > 10290
n = 153, sample mean, xbar = 10586 ; population standard deviation, σ = 2509 ; α = 0.05
Test statistic:
(xbar - μ) ÷ (σ/√(n))
(10586 - 10290) ÷ (2509/√(153))
296 / 202.84062
Test statistic (Z) = 1.46
We obtain the Pvalue :
Decision Region :
Reject H0 ; if Pvalue < α
Pvalue from Z test statistic calculator :
Pvalue = 0.072
Pvalue > α ; Hence, we fail to reject the Null ; there isn't sufficient evidence to support the power company's claim
2.)
H0 : μ = 10290
H0 : μ > 10290
n = 153, sample mean, xbar = 10446 ; population standard deviation, σ = 2509 ; α = 0.02
Test statistic:
(xbar - μ) ÷ (σ/√(n))
(10446 - 10290) ÷ (2509/√(153))
156 / 202.84062
Test statistic (Z) = 0.769
We obtain the Pvalue :
Decision Region :
Reject H0 ; if Pvalue < α
Pvalue from Z test statistic calculator :
Pvalue = 0.221
Pvalue > α ; Hence, we fail to reject the Null ;
B. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.02 level of significance to support the power company claim that the mean amount of electricity for their residents is more than the national average.
A polynomial with a degree of 3
Example: x^{3} +7
Answer:
[tex]x^{3}-5x^{2}+2x+8[/tex]