The correct hypotheses are:
b. [tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) and \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
To determine the appropriate hypotheses for testing the relationship between the type of school attended and verbal reasoning scores for Irish students, we first need to understand the nature of the comparison being made.
We have three groups of students: those who attended secondary school, vocational school, and primary school only. We want to investigate if there is a difference in the mean verbal reasoning scores among these groups.
The null hypothesis [tex](\(H_0\)) states that there is no difference in the mean verbal reasoning scores among the three types of schools, expressed as \( \mu_1 = \mu_2 = \mu_3 \), where \( \mu_1 \), \( \mu_2 \), and \( \mu_3 \)[/tex] are the population means for students attending secondary school, vocational school, and primary school only, respectively.
The alternative hypothesis [tex](\(H_a\)) suggests that at least one of the population means is different from the others, expressed as \( \mu_1, \mu_2, \mu_3 \)[/tex] are not all equal.
Option b correctly represents these hypotheses:
[tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]
This formulation allows for the testing of differences in mean verbal reasoning scores across the three types of schools. The null hypothesis assumes equality among the means, while the alternative hypothesis considers the possibility of inequality.
Each CD in a store costs $10, and each book costs $6. If you want to spend exactly $32, write an equation in standard form modeling this situation. Let c represent the number of CDs you buy, and b represent the number of books you buy.
Final answer:
To model the situation with an equation, use the quantities of CDs and books as variables c and b, and their prices to create the equation 10c + 6b = 32, which represents spending exactly $32.
Explanation:
To create an equation modeling the situation where you want to spend exactly $32 on CDs and books, we need to use the given prices for each item. Let c represent the number of CDs you buy at $10 each, and let b represent the number of books you buy at $6 each.
The total amount spent will be the sum of the amount spent on CDs and the amount spent on books. Using the price of each item, we can write the following equation:
10c + 6b = 32
This equation can now be written in standard form, which is Ax + By = C, where A, B, and C are integers, and A is non-negative. Therefore, our equation in standard form is:
10c + 6b = 32
The following is an illustration of a regular polygon:
Answer:
False
Step-by-step explanation:
A regular sided polygon means all the sides have the same length and all angles the same size. This polygon has 2 sides the same length, not 3 sides the same length, so it cannot be regular.
What is the probability for flipping a tail with a coin and rolling a four with a die
If there are 25,682 people living in Jarvieville in 2015, and the population increases 20% each year...
a) write the equation to use to predict future years
b) how many people will there be in this town in the year 2018?
Answer:
[tex]f(x)=25,682(1.2)^{t}[/tex]
44378.496=44,379
Step-by-step explanation:
We can write the equation using a growth equation [tex]f(x)=P(1+r)^{t}[/tex] where:
P is the starting valuer is the percent or rate as a decimalt is yearsWe will substitute into the formula P=25,682, r=0.2 and t =3 for 3 years since 2018 is 3 years after 2015.
[tex]f(x)=25,682(1+0.2)^{3}[/tex]
[tex]f(x)=25,682(1.2)^{3}[/tex]
[tex]f(x)=44378.496[/tex]
The graph of an absolute value function opens down and has a vertex of (-3,0).
The domain of the function is ?
The range of the function is ?
The domain of the function is:
All real numbers i.e. (-∞,∞)
The range of the function is:
(-∞,0]
Step-by-step explanation:It is given that:
The graph of an absolute value function opens down and has a vertex of (-3,0).
This means that the graph of the function increases continuously in the interval (-∞,-3] and takes maximum value 0 when x= -3 and then decreases continuously in the interval (-3,∞).
Domain of a function--
It is the set of all the x-values for which a function is defined i.e. it is the set of all the values of the independent variable for which the function is defined.
Range of a function--
It is the set of all the values attained by a function.
We know that a absolute value function is defined all over the real line i.e. the domain of the function is the set of all the real values i.e. (-∞,∞).Also, the function takes all the value between -∞ and 0 and 0 is included.Hence, the range of the function is: (-∞,0].
From the table below, determine whether the data shows an exponential function. Explain why or why not.
Answer:
B
Step-by-step explanation:
a shoes has a length of 11 inches. Which unit conversion fraction should you use to find the length in centimeters?
A. 2.54 cm/1 in
B. 1 cm/2.54 cm
C. 1 in / 2.54 cm
D. 1 in / 1 cm
Answer:
2.54 cm/1 inch
Step-by-step explanation:
We have inches. That is in the numerator. We need to convert to cm. So our conversion factor should have cm in the numerator and inches in the denominator.
1 in = 2.54 cm
Divide both sides by 1 inc
A conversion factor is equal to 1
1 = 2.54 cm/1 inch
The correct unit conversion fraction to convert inches to centimeters is 2.54 cm/1 in. Apply this factor to the length in inches (11 inches) to obtain the length in centimeters (27.94 cm).
Explanation:To convert a length in inches to centimeters, we can use a unit conversion fraction. In this case, because there are 2.54 centimeters in one inch, the correct unit conversion fraction to use is A. 2.54 cm/1 in. This means that we multiply the length in inches by the conversion factor to get the length in centimeters. Here is the step-by-step process for your problem:
Convert the given length to centimeters using the correct conversion fraction : Length in centimeters = Length in inches * Conversion factor Length in centimeters = 11 inches * 2.54 cm/in Length in centimeters = 27.94 cmLearn more about Unit Conversion here:https://brainly.com/question/19420601
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Please answer quickly ill give Brainliest.
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept → (0, b)
Read two points from graph
y-intercept: (0, -3) → b= -3
x-intercept: (-2, 0).
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Substitute:
[tex]m=\dfrac{0-(-3)}{-2-0}=\dfrac{3}{-2}=-\dfrac{3}{2}[/tex]
Therefore we have the equation of a line in slope-intercept form:
[tex]y=-\dfrac{3}{2}x-3[/tex]
Convert to the standard form [tex]Ax+By=C[/tex]
[tex]y=-\dfrac{3}{2}x-3[/tex] multiply both sides by 2
[tex]2y=-3x-6[/tex] add 3x to both sides
[tex]3x+2y=-6[/tex]
Answer: 3x + 2y = -6Answer:
y=mx+b
Step-by-step explanation:
7.6g of sugar is needed for every cake made. How much sugar is needed for 5 cakes
Answer:
38 grams
Step-by-step explanation:
7.6*5=38
What is the scale factor of △UVW to △ XYZ?
Answer:
B. 1/7
Step-by-step explanation:
The triangles are similar, so the ratios of corresponding sides are the same.
... UV/XY = 3/21 = 1/7 . . . . . matches B
_____
When we talk about the ratio "A to B", we usually mean A:B or A/B. There's the possibility that the question could be interpreted to mean, "what factor do I multiply by to get from A to B?" In that case, the result here would be 7, because XY is 7 times the length of UV.
A recursive rule for a geometric sequence is a1=2; an= 4/9 an-1
What is the explicit rule for this sequence?
A recursive rule for a geometric sequence:
[tex]a_1\\\\a_n=r\cdot a_{n-1}[/tex]
---------------------------------------------------
[tex]a_1=2;\ a_n=\dfrac{4}{9}a_{n-1}\to r=\dfrac{4}{9}[/tex]
---------------------------------------------------
The exciplit rule:
[tex]a_n=a_1r^{n-1}[/tex]
Substitute:
[tex]a_n=2\left(\dfrac{4}{9}\right)^{n-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\left(\dfrac{4}{9}\right)^{-1}=2\cdot\left(\dfrac{4}{9}\right)^n\cdot\dfrac{9}{4}\\\\\boxed{a_n=\dfrac{9}{2}\cdot\left(\dfrac{4}{9}\right)^n}[/tex]
What is the 31st term of the arithmetic sequence for -15 -11 -7 -3
Answer:
its -11
Step-by-step explanation:
Bridget drives at a speed of 60 miles per hour. how long will it take to drive 270 miles
Divide the total miles by her speed:
270 miles / 60 miles per hour = 4.5 hours.
What is the amplitude of the function shown in the graph? Enter your answer in the box.
Answer: A = 2.5
Step-by-step explanation:
The highest point is 5.5. The lowest point is 0.5.
[tex]Amplitude (A) = \dfrac{high-low}{2}[/tex]
[tex]A = \dfrac{5.5-0.5}{2}[/tex]
[tex]= \dfrac{5}{2}[/tex]
[tex]= 2.5[/tex]
Please answer this question! Brainliest and thirty points!
Answer:
option c
Step-by-step explanation:
x + 9 - 4x =3 - 2x + 4
=>x + 2x - 4x =7 - 9
=>3x - 4x = -2
=>-x = -2
=>x = 2
Answer:
x=2
Step-by-step explanation:
x+9 -4x = 3-2x+4
The first step is to combine like terms
-3x+9 = -2x+7
Add 3x to each side
-3x+3x+9 = -2x+3x+7
9 = x+7
Subtract 7 from each side
9-7 = x+7-7
2 =x
The price of gold is often reported per ounce. At the end of 2005, this price was $513. At the end of 2015, it was $1060. By what percentage did the price per ounce of gold increase?
Answer:
106.63%.
Step-by-step explanation:
We have been given that at the end of 2005, this price was $513. At the end of 2015, it was $1060.
To find the percentage of the price per ounce of gold increase we will use % increase formula.
[tex]\text{Percent Increase}=\frac{\text{Final value-Initial value}}{\text{Initial value}}\times 100[/tex]
Let us substitute our given values in above formula.
[tex]\text{Percent Increase}=\frac{1060-513}{513}\times 100[/tex]
[tex]\text{Percent Increase}=\frac{547}{513}\times 100[/tex]
[tex]\text{Percent Increase}=1.0662768031189084\times 100[/tex]
[tex]\text{Percent Increase}=106.62768031189084\approx 106.63[/tex]
Therefore, the price of per ounce of gold increased by 106.63%.
Answer:107
Step-by-step explanation:
So if it is incorrect for the other answer this is the answer, so do 1060-513=547, so it increased by that much, then divided 547/513= 1.06627680312 But that rounds up to 7 and since we know that the original was 100% of its amount we would add 100+7 which would be 107%
Triangle QRS is dilated about the origin by a scale factor of 2/3 to create triangle ABC . Are the two triangles congruent?
Answer:
No
Step-by-step explanation:
In a dilation, size is not preserved. Triangles must have the same shape and size in order to be congruent. If it is dilated by 2/3, then it gets smaller, and is therefore not the same size.
Final answer:
Triangle QRS is not congruent to triangle ABC after a dilation of [tex]\frac{2}{3}[/tex], but the two triangles are similar because their corresponding angles are equal and sides are proportional.
Explanation:
The question concerns the concept of congruent and similar triangles in geometry. When triangle QRS is dilated about the origin by a scale factor of [tex]\frac{2}{3}[/tex] to create triangle ABC, the two resulting triangles are not congruent because their corresponding sides are not equal in length. However, they are similar since the angles remain the same and the sides are proportional. Congruent triangles are identical in both shape and size, but similar triangles maintain the same shape while the size can vary in proportion.
What is the range of the data represented by the box plot?
Answer:
The range is 12
Step-by-step explanation:
The range of the data is the largest number minus the smallest number.
The largest number is 17
The smallest number is 5
17-5
12
The range is 12
Which is the equation of the given line?
y=-2
Find the slope of the line between
Answer:
y = -2
Step-by-step explanation:
The y values remain constant through the whole line. It pass through the point where y = -2 so it's equation is:
y = -2
6>d-1 graph it please
Answer:
Step-by-step explanation:
6>d-1
Add 1 to each side
6+1 > d-1+1
7>d
Hi there!
Answer:
D>7
*The answer must have a positive sign and greater than symbol.*
Step-by-step explanation:
First, you switch sides of an equation.
[tex]d-1>6[/tex]
Then, you add by 1 from both sides of an equation.
[tex]d-1+1>6+1[/tex]
And finally, you add by the numbers from left too right.
[tex]6+1=7[/tex]
Final answer is d>7
I hope this helps you!
Have a nice day! :)
-Charlie
:D
Alice paid $21.75 for some packs of rice crackers. If each pack costs $1.75, how many packs did she buy?
We have dollars and dollars per pack, so we divide to get how many packs.
[tex] \dfrac{21.75}{1.75} = \dfrac{2175}{175} = \dfrac{87(25)}{7(25)} = \dfrac{87}{7} \approx 12.4[/tex]
Odd that it's not a whole number of packs; please check the question carefully. Let's say she bought 12 and got some change.
My guess is the question really says Alice spent $22.75, so she bought 13 packs. Again check the question carefully. You don't need us to divide two numbers.
On the first play of the game, the Wildcats gained 8 yd. What integer represents a gain of 8 yd? Enter your answer in the box.
Answer:
+8
Step-by-step explanation:
They gained 8 yards so it is +8.
Answer: + 8
Step-by-step explanation: A gain is considered a good thing. It is represented with a positive integer. Here, the gain is represented by +8, or simply 8.
A recipe for tropical punch calls for 2 cups of pineapple juice and 3 cups of orange juice. Jo creates a drink by mixing 3 cups of pineapple juice with 4 cups of orange juice. How does Jo's drink compare to the tropical punch recipe?
Use the Pic if Needed :)
Answer:
Jo's drink is bigger than the tropical punch, both have more orange juice than pineapple.
Step-by-step explanation:
Tropical punch is 2 cups of pineapple juice and 3 cups of orange juice
We express those numbers is fraction , to get the denominator we add the 2 parts, 2 cups + 3 cups= 5
Then,
pineapple juice=2/5
orange juice=3/5
Drink is 3 cups of pineapple juice with 4 cups of orange juice
Denominator is 3 + 4 = 7
pineapple juice=3/7
orange juice=4/7
Jo's drink is bigger than the tropical punch, both have more orange juice than pineapple.
Which equation has exactly two real and two non real solutions?
Answer:
The first option [tex]x^4-21x^2-100=0[/tex].
Step-by-step explanation:
To have exactly 2 real and two non real solutions, the degree of the polynomial must be a degree 4. Degree is the highest exponent value in the polynomial and is also the number of solutions to the polynomial. This polynomial ha 2 real+2 non real= 4 solutions and must be [tex]x^4[/tex]. This eliminates the bottom two solutions.
In order to have two real and two non real solutions, the polynomial must factor. If it factors all the way like
[tex]x^4-100x^2=0\\x^2(x^2-100)=0\\x^2(x-10)(x+10)=0\\\\x^2=0\\x-10=0\\x+10=0[/tex]
This means x=0, 10, -10 are real solutions to the polynomial. It has no non real solutions. This eliminates this answer choice.
Only answer choice 1 meets the requirement.
Answer:
A. x^4 - 21x^2 - 100 = 0
Marry had 22 3/4 grams of salt. She used 7 1/4 grams to make spinach omelets and 4 7/8 grams to make mushroom omelets. About how much salt does Marry have left? Choose the best estimate.
Answer:
10 5/8
Step-by-step explanation:
We need to subtract (7 1/4 + 4 7/8) from 22 3/4 grams of salt.
We compute the whole numbers and fractions separately:-
7 + 4 = 11
1`/4 + 7/8 = 2/8 + 7/8 = 9/8 = 1 1/8.
So 7 1/4 + 4 7/8 = 12 1/8
Therefore:-
22 3/4 - 12 1/8
22 - 12 = 10
3/4 - 1/8 = 5/8
= 10 + 5/8 = 10 5/8 (answer)
The length of a rectangular is 5 centimeters less then it width. The perimeter of the rectangle is 26
Hi there! :)
Answer:
Length = 4 cm
Width = 9 cm
Step-by-step explanation:
Here's the information we know:
- Perimeter = 26 cm
- Width = x (I just replaced the width by "x" because it's what we are looking for)
- Length = x - 5
Now before we can do anything, you need to know what the formula for the perimeter of a rectangular is: P = (2 × Length) + (2 × Width)
Replace all the information you know in the formula and solve the equation by isolating "x":
P = (2 × Length) + (2 × Width)
26 = ( 2 × (x - 5)) + (2 × x)
Multiply "2" and "x" together → 2 × x = 2x
26 = ( 2(x - 5)) + 2x
Distribute the "2" to the entire parentheses → 2 × x = 2x & 2 × -5 = -10
26 = 2x - 10 + 2x
Add similar terms together → 2x + 2x = 4x
26 = 4x - 10
Add 10 to each side of the equation → 26 + 10 = 36
36 = 4x
Divide each side of the equation by 4 → 36 ÷ 4 = 9
9 = x ⇒ Measure of the width
Since the lenght is 5 centimeter less than the measure of the width, in order to find the measure of the length you'll need to subtract "5" from the measure of the width, which is "9":
9 - 5 = Length rectangle
9 - 5 = 4 ⇒ Length rectangle
There you go! I really hope this helped, if there's anything just let me know! :)
Postal carrier can deliver 130 houses and 2.5 hour. At this rate how many hours will it take to deliver 312 at houses
First, you much find out how many houses are deliverd in 1 hour.
130/2.5=52
So 52 houses are delivered in 1 hour. Now, divide that by 312.
312/52=6
It would take 6 hours to deliver 312 houses.
The nicotine content in cigarettes of a certain brand is normally distributed with mean
(in milligrams) m and standard deviation s = 0.1. The brand advertises that the mean
nicotine content of their cigarettes is 1.5, but measurements on a random sample of 400
cigarettes of this brand gave a mean of x = 1.52. Is this evidence that the mean nicotine
content is actually higher than advertised? To answer this, test the hypotheses
H0: m = 1.5, Ha: m > 1.5
at significance level a = 0.01. You conclude
A) that H0 should be rejected.
B) that H0 should not be rejected.
C) that Ha should be rejected.
D) that there is a 5% chance that the null hypothesis is true.
Through hypothesis testing, we cannot reject the null hypothesis at the 1% level of significance. Thus, there is no strong evidence to suggest that the mean nicotine content is greater than what is advertised.
Explanation:The subject here is statistics, specifically hypothesis testing. For this problem, we are asked to test the null hypothesis H0: m = 1.5 against the alternative hypothesis Ha: m > 1.5 at 1% level of significance.
Using the given data, we calculate the test statistic (z) using the formula: z = (x - µ) / (s/√n), where x is the sample mean, µ is the population mean, s is the standard deviation, and n is the sample size. Substituting the given values, we get z = (1.52 - 1.5) / (0.1/√400) = 2.
The z-score at 0.01 level of significance is -2.33 on the left and 2.33 on the right. As our test statistic (2) falls within this range, we fail to reject the null hypothesis (H0: m = 1.5). This suggests that there's no strong evidence to support that the mean nicotine content is greater than advertised.
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Which of the following terms best describes three points that all lie in a straight line?A. CollinearB. CongruentC. EqualD. Midpoint
I would appreciate a description of this as well.
*Take math seriously or you gone have to retake this subject*
Answer:
A. Collinear
Step-by-step explanation:
three points that all lie in a straight line
A. Collinear- means along the same line
B. Congruent - means the same
C. Equal = means the same
D. Midpoint= means the middle
Answer by YourHope:
Hi! :)
Which of the following terms best describes three points that all lie in a straight line?
I would say A. Collinear!
:)
Given that SU≅UT and SV>VT, identify a two-column proof that proves m∠SUV>m∠TUV.
Answer: Choice B
We start with SU = UT being given, and so is SV > VT.
The second line is UV = UV by the reflexive property to help us use the converse of the hinge theorem next.
The hinge theorem basically says that the more open an angle is, the larger the opposite side will be (the side opposite from the angle that varies). Imagine a door opening and closing. The further open it gets, the longer the rope will be that connects the door handle to the frame. Going in reverse, the converse says that if the opposite side of the angle gets bigger, then the angle itself gets bigger as well. The hinge theorem is handy to help compare two sides even if we don't know their exact lengths (we can figure out which side is larger than the other)
The conditions given that SU is congruent to UT and SV is greater than VT create a scenario where we can prove that the measure of angle SUV is greater than the measure of angle TUV.
Explanation:Given that SU≅UT means that segment SU is congruent to segment UT, and SV>VT meaning that segment SV is greater than segment VT, this sets up two important conditions for the triangle SUV. First, as SU is congruent to UT, this implies that ∠SUV is congruent to ∠TUV due to the Base Angles Theorem (If two sides of a triangle are congruent (equal), then angles opposite these sides are congruent). However, SV>VT creates an inequality which contradicts this, pointing towards the fact that ∠SUV is greater than ∠TUV.
Proof:
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