Step-by-step explanation:
Draw a rectangle. If the length is 3 inches longer than its width, we can write the width as "w" and the length as the width + 3
Area is (width)(Length) = (width)(width+3)
W
----------
| |
| |
| | L = w+3
| |
| |
-----------
A = (w+3)(w)
A = w2 + 3w = 108.
(Problem states that area is 108 sq in)
Need to solve this quadratic equation
w2 + 3y - 108 = 0
Factor:
(w - 9) (w + 12) = 0
So
w - 9 = 0. or. w + 12 = 0
Solve these and get
w = 9. or. w = -12
Only one that makes sense in real life is the poitive one.
So the dimensions are
Width = 9 inches
Length = 12 inches
hope this helped-nia.
a fish tank 60 litres of water round to 1 significant figure
40 litres of water rounded to 1 significant figure is removed from the tank
work out the upper bound of the water left in the tank
The upper bound of the volume of water left in the fish tank is 20 liters.
In the given statement is :
A fish tank contains 60 liters of water, rounded to 1 significant figure. 40 liters of water, rounded to 1 significant figure, are removed from the tank.
Work out the upper bound of the volume of water left in the fish tank.
Now, According to the question:
Initial water in tank = 60 liters
Amount of water removed = 40 liters
Hence, To calculate the upper bound of the volume of water left in the fish tank;
= 60 - 40
= 20 liters
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There are 9 players on a youth baseball team. To create the lineup, the coach chooses three players to play pitcher, catcher, and first base. How many ways can the coach choose these three positions?
Step-by-step explanation:
how many ways can the coach make out the batting order? 9! = 9 · 8 · 7 · 6 · 5 ·4 · 3 · 2 · 1 = 362,880 .
Please help I'm studying my next grade.
63+48÷(23-11)×38
Answer:
215
Step-by-step explanation:
To solve this expression, we must first use the order of operations. We begin with the parentheses and evaluate 23-11, giving us 12. Then, we divide 48 by 12, which equals 4. Finally, we multiply 4 by 38, resulting in 152. We add this to 63, giving us a final answer of 215. Thus, the solution to 63+48÷(23-11)×38 is 215.
4. Attractiveness and a Great Sense of Humor (Based on Exercise 9.21, part a) In the Preview for Chapter 9 of the textbook, the authors discussed a study by McGee and Shevlin (2009) demonstrating that an individual’s sense of humor had a significant effect on how the individual was perceived by others. In one part of the study, female college students were given brief descriptions of a potential romantic partner. The fictitious male was described positively and, for one group of participants, the description also said that he had a great sense of humor. After reading the description, each participant was asked to rate the attractiveness of the man on a seven-point scale from 1 (very unattractive) to 7 (very attractive) with a score of 4 indicating a neutral rating.
a. Write the null and alternative hypotheses to determine if the females who read the “great sense of humor” description gave the potential partner an average attractiveness rating that was higher than neutral (μ = 4).
Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,
μ ≤ 4
Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.
We have,
The null and alternative hypotheses to determine if the females who read the "great sense of humor" description gave the potential partner an average attractiveness rating that was higher than neutral (μ = 4) can be written as:
Null Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is not higher than neutral,
μ ≤ 4
Alternative Hypothesis: The average attractiveness rating given by females who read the "great sense of humor" description is higher than neutral, μ > 4.
Thus,
The null hypothesis states that the mean attractiveness rating of males who are described positively and with a great sense of humor is not significantly different from a neutral rating of 4.
The alternative hypothesis states that the mean attractiveness rating of such males is significantly higher than a neutral rating of 4.
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marking as brainlist pls help
Which integers are opposites?
14 and –4
17 and –17
32 and –23
15 and –51
Answer:
A
Step-by-step explanation:
The opposite of an integer is the number on the opposite side of the number line with the same distance from zero. So, the integers that are opposites are 14 and -14, 17 and -17, 32 and -32, and 15 and -15. This is because these pairs have the same absolute value but different signs. For instance, the absolute value of 14 is 14, and the absolute value of -14 is also 14. Therefore, -14 is the opposite of 14. Similarly, -17 is the opposite of 17 and so on.
Answer:
a
Step-by-step explanation:
got it right on edge
I need help with this please give me reason and explain pls
Answer: 18º
Step-by-step explanation:
a + 126º = 180º (adj. ∠s on st. line)
a = 54º
Let the adjacent angle next to b be c.
a + c = 180º (int. ∠, AB//CD)
54º + c = 180º
c = 126º
108º + x = 126º (ext. ∠ of Δ)
x = 18º
Find the area of each triangle.
The area of the triangle is 2√2 square units.
This is a right triangle, and the base (the side opposite the right angle) has a length of 2√2.
We can use the Pythagorean theorem to find the length of the other two sides:
x² + x² = (2√2)²
2x² = 8
x² = 4
x = 2
So the two other sides have a length of 2.
Now we can use the formula for the area of a triangle:
Area = (1/2) × base × height
In this case, the base is 2√2 and the height is 2, so we have:
Area = (1/2)×2√2 ×2
Area = 2√2
Therefore, the area of the triangle is 2√2 square units.
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may someone help me of which one to pick
Answer:
Elena
Step-by-step explanation:
Sorry we have to see the complement first because it is of 90° jjust let the second w go we will do that later we can find the value of w by choosing elena
The circumference of a circle is 17.584 inches. What is the circle's area?
Step-by-step explanation:
Given the circ , you can find the diameter....then the radius
circ = pi * d
17.584 = pi * d
d = 5.597 in then radius = 1/2 d = 2.798
AREA = pi r^2 = pi * 2.798^2 = 24.6 in^2
Determine whether or not it defines a function. Pease shows steps so I understand the answer.
The requried, justification for the given function has been shown below.
(a) Yes, R₁ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is 0 in this case.
(b) No, R₂ does not define a function. For some values of n, there may be multiple animals with n legs, so there is no unique output for each input.
(c) Yes, R₃ defines a function. Each element in the domain is mapped to a unique element in the codomain, which is the remainder of n divided by 5.
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Jordan has gone into the nut business. He wants to make a mixture of walnuts and cashews that cost $1.00 per pound. How many pounds of walnuts that cost $0.80 per pound must be mixed with 8 pounds of cashews that costs $1.25 per pound to make his mixture of nuts cost $1.00 per pound?
A. 16 lbs
b. 11 lbs
c. 20 lbs
d. 10 lbs
Answer:
The answer is (d) 10 lbs.
Step-by-step explanation:
Let's start by using the weighted average formula:
weighted average price = (price of first item x weight of first item + price of second item x weight of second item) / total weight
Let x be the number of pounds of walnuts needed.
The total weight of the mixture is x + 8 pounds.
The price of the walnuts is $0.80 per pound, and the price of the cashews is $1.25 per pound.
We want the mixture to cost $1.00 per pound.
Using the formula, we get:
1.00 = (0.80x + 1.25(8)) / (x + 8)
Simplifying, we get:
1.00(x + 8) = 0.80x + 10
1.00x + 8.00 = 0.80x + 10.00
0.20x = 2.00
x = 10
Therefore, Jordan needs to mix 10 pounds of walnuts with 8 pounds of cashews to make a mixture that costs $1.00 per pound.
Please help me with part (b) and (c) pleaseeee
thank youuu
The answers are explained in the solution.
Given are lines drawn in a coordinate plane, we need to identify the equations,
So, we have,
y = 2x – 4 = r
y = 2x + 4 = p
This is because these lines are parallel and have same slope, also the y-intercept is -4 and 4,
y = x = n
y = -x = s
This is also because, the line of y = x passes from origin.
b) We can use a translation to map the line p or r onto the line r or p.
c) We can use an axial symmetry in the y-axis to map the line n or s onto the line s or n.
d) The line s or n is mapped onto itself under central symmetry in the point (0, 0).
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How many times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284
The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.
Here, we have,
given that,
the value represented by the digit 8 in the number 8,342
and, the value represented by the digit 8 in the number 284.
now, we have to find that how many times greater is the value.
so, we have to differentiate the value represented by the digit 8 in the number 8,342 with the value represented by the digit 8 in the number 284.
so, we get,
the value represented by the digit 8 in the number 8,342 is 8000
and, the value represented by the digit 8 in the number 284 is 80
so, difference between them is:
8000 - 80
=7980
Hence, The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representation of the inequality –3(2x – 5) < 5(2 – x) are :
-6x + 15 < 10 - 5x
x < 5
Given an inequality,
–3(2x – 5) < 5(2 – x)
We have to find the equivalent representation of the inequality.
(-3)(2x) - (-3)(5) < (5)(2) - (5)(x)
-6x + 15 < 10 - 5x
-6x + 5x < 10 - 15
-x < -5
x < 5
Hence the correct options are -6x + 15 < 10 - 5x and x < 5.
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A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the
theoretical probability of 5 students from your school being selected as contestants out of 8 possible contestant spots?
P(5 students selected) =
(Type an integer or decimal rounded to three decimal places as needed.)
Answer:
120/30*29*28*27
Step-by-step explanation:
A Pew Research Center poll of 1060 teens aged 13 to 17 showed that 57% of them have made
new friends online. Use a 0.01 significance level to test the claim that half of all teens have
made new friends online.
Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.
For test the claim that half of all teens have made new friends online, we can use a hypothesis test.
Null hypothesis:
The proportion of teens who have made new friends online is equal to 0.5.
Alternative hypothesis:
The proportion of teens who have made new friends online is not equal to 0.5.
We will use a one-sample proportion test with a significance level of 0.01.
For calculate the test statistic, we can use the formula:
z = (p - P₀) / sqrt(P₀ * (1 - P₀) / n)
where p is the sample proportion, P₀ is the hypothesized proportion (0.5), and n is the sample size.
Using the given information, we have:
p = 0.57
P₀ = 0.5
n = 1060
Plugging these values into the formula, we get:
z = (0.57 - 0.5) / sqrt(0.5 x 0.5 / 1060)
z = 4.39
Hence, Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.
Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than half of all teens have made new friends online.
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explain why the graph would look like the line y=x if you graph it
The graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
How to explain the informationBoth the numerator and denominator of f(x) = x(x+5)(x+3) / (x+3)(x+5) cancel out the factors (x+3) and (x+5), giving us a simplified expression for the function, f(x) = x.
A line with a slope of 1 passes through the origin in an upward direction. When we examine the graph of y=x, which is a straight line passing through the origin with a slope of 1, it becomes apparent that adding 1 to x also adds 1 to y.
Since the simplified expression is merely f(x) = x, we can deduce that the graph of this function follows a linear path passing through the origin with a slope of 1.
In conclusion, the graph of f(x) = x(x+5)(x+3) / (x+3)(x+5) bears resemblance to the line y=x since both plots share similar linear characteristics.
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Gina wants to go to the water park with her friends. They have a total of www dollars to buy 555 tickets. Each ticket costs 151515 dollars. Select the equation that matches this situation. Choose 1 answer: Choose 1 answer: (Choice A) 5 = 15 \times w5=15×w5, equals, 15, times, w A 5 = 15 \times w5=15×w5, equals, 15, times, w (Choice B) w = 15 +5w=15+5w, equals, 15, plus, 5 B w = 15 +5w=15+5w, equals, 15, plus, 5 (Choice C) w = 5 \times 15w=5×15w, equals, 5, times, 15 C w = 5 \times 15w=5×15
The equation which correctly represents the given situation as required to be determined is; Choice C; w = 5 × 15.
Which equation correctly matches the given situation?It follows from the task content that the equation which correctly represents the Given situation is to be determined.
Since the intention is to buy 5 tickets in which case; each ticket costs 15 dollars; we have that;
Since the total amount of dollars they have is w dollars; The equation which holds true for the situation is; w = 5 × 15.
Consequently, answer choice C; w = 5 × 15 is correct.
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Use the image to determine the type of transformation shown.
Graph of polygon VWXYZ with W at point 2 comma 4. A second polygon V prime W prime X prime Y prime Z prime with W prime at point negative 2 comma 4.
Reflection across the x-axis
Reflection across the y-axis
270° counterclockwise rotation
Horizontal translation
The image is reflected over the y-axis. Then the correct option is B.
Given that:
Point of the polygon VWXYZ, W(2, 4)
Point of the polygon V'W'X'Y'Z', W'(-2, 4)
The translation does not change the shape and size of the geometry. But changes the location.
The reflection does not change the shape and size of the geometry. But flipped the image.
The point W' can be obtained by reflecting the shape across the y-axis.
Thus, the correct option is B.
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The missing diagram is given below.
Wyatt goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 6% is applied to the bill. Wyatt decides to leave a tip of 17% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Wyatt paid.
Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.
We have,
The amount of tax applied to the bill is 6% of the subtotal, or 0.06x.
The total bill (including tax) is.
x + 0.06x = 1.06x
To find the amount of tip Wyatt left on the total bill, we need to multiply the total bill by 17% (or 0.17):
0.17(1.06x) = 0.1802x
The expression in terms of xx that represents the total amount that Wyatt paid is:
= x + 0.06x + 0.1802x
Simplifying the expression by combining like terms.
Total amount = 1.2422x
Thus,
Wyatt paid 1.2422 times the amount of subtotal x, including tax and tip.
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Find the mode for the set of data: 18, 7, 15, 11, 7, 7
Answer:
7
Step-by-step explanation:
7, 7, 7, 11, 15, 18
The mode is the number that appears most.
Answer: 7
Answer:
7
Step-by-step explanation:
The mode is the most frequently occurring value in a set of data. In this case, the number 7 occurs twice, which is more than any other number, so the mode is 7. It is worth noting that if there were no values that occurred more than once, then there would be no mode for the data set. In this case, the data set has a single mode, but it is possible for a data set to have multiple modes if there are multiple values that occur with the same highest frequency.
The graph of a quadratic function with vertex (0, 3) is shown in the figure below.
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
We have,
From the given quadratic function,
We see that,
The x-values are -∞ to ∞
The y-values are from 3 to ∞
Now,
The x-values are called the domain.
The y-values are called the range.
Thus,
The domain of the function is (-∞, ∞.)
The range of the function is {3, ∞}.
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How many coupons can be generated
The number of coupon codes that can be generated is given as follows:
247,808 coupon codes.
What is the Fundamental Counting Theorem?The Fundamental Counting Theorem states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both.
This can be extended to more than two events, where the number of ways to do all the events is the product of the number of ways to do each individual event, according to the equation presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
The codes are composed as follows:
Two letters -> each with 22 options, as letters can be repeated.Three digits -> each with 8 options, as digits can also be repeated.Thus the total number of codes is obtained as follows:
N = 22² x 8³
N = 247,808 coupon codes.
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On the 6th grade math test, twelve students had a score of 80 points. Eight students had a score of 88 points.
What was the class average?
The requried class average is 83.2 points.
To find the class average, we need to calculate the total number of points earned by all the students and divide by the total number of students.
The 12 students who scored 80 points earned a total of 12 × 80 = 960 points.
The 8 students who scored 88 points earned a total of 8 × 88 = 704 points.
The total number of points earned by all the students is 960 + 704 = 1664 points.
The total number of students is 12 + 8 = 20.
To find the class average, we divide the total number of points by the total number of students:
average = total points / total students
average = 1664 / 20
average = 83.2
Therefore, the class average is 83.2 points.
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find the slope of the points passing through (4,-1) and (4,-5)
Answer:
A(4;-1)
B(4;-5)
S=yB-yA/ xB-xA
= -5+1/ 4-4
=-4/0
impossible
help me pls right answer onlyy. algebra
The slope of a linear function of the table of values given above is calculated as: m = 3.
How to Find the Slope of a Linear Function?The slope of a linear function is calculated as change in y over change in x. Note that f(x) is also the same as variable "y".
To calculate the slope, pick any two pairs of values from the table given, i.e. (2, 3) and (3, 6):
Slope of the linear function (m) = change in y / change in x = 6 - 3 / 3 - 2
Slope (m) = 3/1
Slope (m) = 3.
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6. A vehicle has a mass of 1295 kg and uses petrol. Another vehicle has a mass of 1290 kg and uses diesel fuel.
1 L of petrol has a mass of 737 g.
1 L of diesel has a mass of 820 g.
How many litres of fuel will result in the two vehicles having the same mass? Round to the nearest tenth of a litre.
When about 60.2 liters of fuel are added to each car, the two vehicles will have the same mass.
How to determine the many liters of fuel will result in the two vehicles having the same massLet x be the number of liters of fuel needed for the two vehicles to have the same mass.
The first vehicle's total mass with fuel is: 1295 + 0.737x
The total weight of the second vehicle with gasoline is: 1290 + 0.820x
We want the two masses to be equal so that we may equalize the two expressions and solve for x:
295 + 0.737x = 1290 + 0.820x
0.083x = 5
x = 60.24
Therefore, the two vehicles will have the same mass when approximately 60.2 liters of fuel have been added to each vehicle.
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Please answer the question
Answer: C. 96
Step-by-step explanation:
I took 8×3×4=96
Since the height is 5 in and it already took up one inch, that means just 4 more inches to go hence the 4 in the multiplication.
What are the domain and range of the inequality ys √x-1-4?
the domain and range of the inequality are,
x ≥ 1 and y ≥ - 4
The inequality is:
⇒ y ≤ √(x - 1) - 4
Now, To find:
The domain and range of the given inequality.
Solution:
We have,
⇒ y ≤ √(x - 1) - 4
The related equation is:
⇒ y ≤ √(x - 1) - 4
This equation is defined if:
√x - 1 ≥ 0
x ≥ 1
In the given inequality, the sign of inequality is <, it means the points on the boundary line are not included in the solution set.
So, the domain of the given inequality is, x ≥ 1
We know that,
√(x - 1) ≥ 0
√(x - 1) - 4 ≥ - 4
y ≥ - 4
So, the range of the given inequality is, y ≥ - 4
Therefore, the correct option is C.
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