Using the roller coaster as an example, draw a right triangle.
The equation used to find the horizontal distance: h² = 30² - 25².16.58 feet is the horizontal distance.What are ways to arrive at the equation?25 feet is listed as the height.The answer to the whole question is that the roller coaster measures 30 feet long.Use h to symbolize the horizontal distance.
The following expression can be used to get h given that roller coaster serves as a representation of the hypotenuse side length.
30² = h² + 25².
Assemble similar phrases.
h² = 30² - 25².
horizontal separation
In (a), there is:
h² = 30² - 25².
This results:
h² = 275
Take both sides' roots.
h = 16.58
Consequently, 16.58 feet are the horizontal distance.
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5. A pound cake recipe calls for 3/4 cups of milk
and makes 4 1/2 servings. How many cups of milk
are needed for 16 servings?
8/3 or 2 2/3 cups of milk are needed for 16 servings.
What is the unitary method?
The unitary method is a technique for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit.
Given that 3/4 cups of milk needs to make 4 1/2 servings
Converting mixed fraction into improper fraction:
or, 3/4 cups of milk needs to make 9/2 servings.
To make 9/2 servings, needs 3/4 cups of milk
Applying unitary method:
To make 1 servings, needs (3/4)/(9/2) cups of milk.
To make 16 servings, needs [(3/4) × 16]/(9/2) cups of milk.
Simplify the numerical expression:
[(3/4) × 16]/(9/2)
= [3 × 4]/(9/2)
= [3 × 4 × 2] /9
= 8/3
Convert improper fraction into mixed fraction:
=(6 + 2)/3
= 6/3 + 2/3
= 2 2/3
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1) Kathy is 12 years old and Ben is 16 years old. How many years ago was Ben three times as old as Kathy?
2) Find z if 1 4/11 of z is 45
3) Emma is 10 years old. She asked her father how old he is and he said, "When you are my age, I will be 70." How old is Emma's father?
4) Jame's dog Buddy is 2 years older than his cat Fluffy. Three years ago, Buddy was three times as old as Fluffy. How old are Buddy and Fluffy now?
5) The sum of x and y age is 60. In six years, y will be eight times as old as x will be. How old is x?
If a woman making $35,000 a year receives a cost-ofliving increase of 2.9%, what will her new salary be?
Answer:
36,015.
Step-by-step explanation:
To calculate the cost-of-living increase, you would first multiply the current salary by the percentage increase: $35,000 * 0.029 = $1,015.
Then, to find the new salary, you would add the cost-of-living increase to the current salary: $35,000 + $1,015 = $36,015.
So, the woman's new salary would be $36,015 per year.
Help on this ez math table question
Answer:x=-3
Step-by-step explanation:
if you were to plug in -3 for f(x) you would get, f(-3)=1/3(-3) +2, which then equals f(-3)=-1+2, so f(-3)=1
Now you do the same thing for g(x), so you would get g(-3)=2^(-3+3), meaning you first add -3 and 3 leaving you with g(-3)=2^0, which is equal to 1.
f(-3)=1=g(-3)
Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 7cm,24cm
Answer:
The length of the hypotenuse is 25 cm.
Step-by-step explanation:
We can use the Pythagorean theorem to find the hypotenuse.
Pythagorean theorem states
[tex]a^2+b^2=c^2[/tex]
Where [tex]a[/tex] and [tex]b[/tex] are the legs or sides of the triangle.
The hypotenuse is [tex]c[/tex].
We can solve for [tex]c[/tex] by taking the square root of both sides of the equation.
[tex]c=\sqrt{a^2+b^2}[/tex]
We are given
[tex]a=7\\b=24[/tex]
Lets evaluate [tex]c.[/tex]
[tex]c=\sqrt{7^2+24^2}[/tex]
[tex]c=\sqrt{49+b^2}[/tex]
[tex]c=\sqrt{49+576}[/tex]
[tex]c=\sqrt{625}[/tex]
[tex]c=25[/tex]
A rating/review would be much appreciated. Wish you a happy holiday season!
Which integer has a greater value? -2 or -5?
The integer has a greater value is -2
What is the integer with a greater value?An integer is a whole number (rather than a fraction) that can be positive, negative, or zero. Positive numbers, negative numbers, and zero are all examples of integers. 'Integers include both whole and negative numbers. This means that if we add negative numbers to whole numbers, we get a set of integers.
An integer is a number that has no decimal or fractional part and can be negative or positive, including zero. In this case, the numbers are -5 and -2. It should be noted that -2 is more than -5.
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Suppoe that 19% of people have a dog,24% of people have a cat , and 14% of people have both
19% of people have a dog,24% of people have a cat , and 14% percentage of people have both 62% of people have either a dog or a cat.
To find the percentage of people that have either a dog or a cat, we need to add the percentage of people that have a dog to the percentage of people that have a cat.
19% + 24% = 43%
Therefore, 62% of people have either a dog or a cat.
43% of people have either a dog or a cat, but do not have both. We can find this by subtracting the percentage of people that have both a dog and a cat from the total percentage.
43% - 14% = 29%
Therefore, 29% of people have a dog or a cat, but not both.
The complete question is:
Suppoe that 19% of people have a dog,24% of people have a cat , and 14% of people have both dog and cat.
What percentage of people have either a dog nor a cat?
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leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes startfraction 2 over 3 endfraction. of her daily calories at dinner. if x represents the calories consumed at dinner, which statements describe the situation? check all that apply.leena consumed 1,500 calories at dinner.the equation startfraction 2 over 3 endfraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x 400 350)
The correct statements are:
1) Leena consumed 1,500 calories at dinner.
2) The equation 2/3(x + 400 + 350) = x
In this question we have been given Leena consumes 400 calories at breakfast and 350 calories at lunch. she consumes 2/3 of her daily calories at dinner.
We need to select a statement that describes the situation if x represents the calories consumed at dinner.
Let x be the calories consumed at dinner.
Leena consumes 400 calories at breakfast and 350 calories at lunch.
So, the daily calories consumed by her:
400 + 350 + x
Given that she consumes 2/3 of her daily calories at dinner.
From given conditions we get an equation,
x = 2/3(x + 400 + 350)
3x = 2(x + 750) ............(multiply both sides by 3)
3x = 2x + 1500
3x - 2x = 2x + 1500 - 2x ...............(subtract 2x from both sides)
x = 1500 calories
Therefore, Leena consumed 1500 calories at dinner.
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If f(2x + 5) = 6x + 19, find fof(2).)
Answer:
x = 4.083
Step-by-step explanation:
6(2x+5)+19=0
12x+30+19=0
12x+49=0
12x=-49
x=4.083
Answer:
f(2x + 5) = 6x + 19
= 6(2x + 5) + 19
= 12x + 30 + 19
= 12x + 49
f(2) = 12x + 49
= 12(2) + 49
= 73
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-on her way home from the school board meeting, kelly fills up her car. she likes the idea of using gasoline with ethanol, but thinks her car can only handle 50% ethanol. at the gas station, she can use regular gas with 15% ethanol or e78 fuel with 78% ethanol. how many gallons of each type of fuel should kelly use if she wants to fill up her car with 9 gallons of fuel containing 50% ethanol? 5 gallons of regular gas with 15% ethanol; 4 gallons of e78 fuel with 78% ethanol 6 gallons of regular gas with 15% ethanol; 3 gallons of e78 fuel with 78% ethanol 4 gallons of regular gas with 15% ethanol; 5 gallons of e78 fuel with 78% ethanol 3 gallons of regular gas with 15% ethanol;
She'll need 4 gallons of 15% ethanol gasoline and 5 gallons of 78% ethanol gasoline.
What is expression?An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.
Here,
The number of gallons required of both kind would be as follows:
4 gallons having 15% ethanol
5 gallons having 78% ethanol
Given that,
The 2 kinds of gases are:
One with 15% ethanol
Other with 78% ethanol
Given that,
The gases(ethanol and gasoline) are diluted in a such a manner that it involves a total of only 50% ethanol.
Number of gallons she wants to use = 9
This shows that only 50% of 9 gallons i.e. 4.5 gallons of ethanol can be used.
Assuming x being the gasoline's measure that is diluted with 15% ethanol.
Now,
The gasoline's measure that is diluted with 78% ethanol would be = 9 - x gallons
Therefore,
x × 15% + (9-x) × 78% = 4.5
On solving, we get
x = 4 gallons
Thus,
The measure of gallons having 15% ethanol = 4
The measure of gallons having 78% ethanol = (9 - x)
= (9 - 4)
= 5 gallons
She will use 4 gallon of 15% ethanol gas and 5 gallon of 78% ethanol gas.
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sam and taylor own and operate a car wash service. sam cleans the interior of each car and taylor cleans the exterior. the time it takes sam to finish the interior has a mean of 202020 minutes with a standard deviation of 6.46.46, point, 4 minutes. the time it takes taylor to finish the exterior has a mean of 181818 minutes with a standard deviation of 4.84.84, point, 8 minutes. both of their finishing times are approximately normally distributed. suppose we select a car at random, and define the random variable ddd as the difference between their finishing times. we can assume that their times are independent. find the probability that they finish within 101010 minutes of each other.
They have a 0.77 chance of finishing within 10 minutes of each other.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
Here,
mean of the difference between their times is the difference of the expected (or mean) times for each person,
=20-18
=2
standard deviation,
=√((6.4)²+(4.8)²)
=8
The probability,
=0.77
The probability that they finish within 10 minutes of each other is 0.77.
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Solve the equation.
-5x³+x+2x³=7-3x³
Answer:3.3
Step-by-step explanation:
how do you ensure accurate predictions using data correlation? which are the most effective methods?
The only kind of data generated by observational research is correlations or patterns in the data that have been observed. By using correlations, one variable's value can be used to predict the value of another.
Explanation:
Accurate predictions using data correlation can be ensured by using a variety of methods. Firstly, it is important to ensure that the data is free from errors and is of high quality. This can be done by cleaning and validating the data to remove any inconsistencies and outliers. Secondly, it is important to analyze the data thoroughly and identify any patterns or trends. Furthermore, it is beneficial to use appropriate statistical tests and algorithms such as linear regression, logistic regression, and decision trees to identify the predictive relationships between the variables. Finally, it is important to evaluate the model’s performance to determine the accuracy of the predictions.
The most effective methods for ensuring accurate predictions using data correlation are:
1. Perform Exploratory Data Analysis: Exploratory data analysis is an essential step in any predictive modeling process. It involves exploring the data to identify patterns, trends, and relationships within the data. This helps to identify any potential issues or biases within the data that could affect the accuracy of predictions.
2. Use Statistical Tests: Statistical tests can be used to measure the strength of the relationship between two variables. These tests can help to identify which variables are most strongly correlated with each other and can help to determine which variables should be used in a predictive model.
3. Use Machine Learning Algorithms: Machine learning algorithms can be used to create predictive models that can identify and learn patterns in the data. These algorithms are particularly effective at identifying complex relationships between variables that may not be identified by statistical tests.
4. Validate Predictions: Predictions should always be validated to ensure that they are accurate and reliable. This can be done by comparing the predictions against known outcomes or by testing the model on a separate data set.
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what formula is used to gain information about an individual data value when the variable is normally distributed?
The formula used to gain information about an individual data value when the variable is normally distributed is called the z-score formula.
It is used to calculate how many standard deviations a value lies above or below the mean of the data set. The formula is:
z-score = (x - μ) / σ
where x is the data value, μ is the mean of the data set, and σ is the standard deviation of the data set.
To find the z-score of an individual data value when the variable is normally distributed, use the z-score formula. This formula subtracts the mean (μ) from the data value (x) and divides by the standard deviation (σ). This calculation will give you the number of standard deviations the data value lies above or below the mean.
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The coordinates of the vertices of quadrilateral ABCD are A(-5, 1), B(-2, 5), C(5, 3), and D(2, -1).
Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is!
Quadrilateral ABCD is
0
the slope of BC is
the slope of CD is!
because
¹0
and the slope of AD is!
The slope of AB is 4/3, the slope of BC is -2/7, the slope of CD is 4/3 and the slope of AD is -2/7. The Quadrilateral ABCD is a parallelogram because both pairs of opposite sides are parallel in a parallelogram.
The vertices of Quadrilateral ABCD are A(−5, 1) , B(−2, 5) , C(5, 3) , and D(2, −1) .
The slope between 2 points is:- m=(y2-y1) / (x2-x1)
The slope of AB :
m= (5-1) / (-2-(-5))
m= 4/3 ........................(1)
The slope of BC :
m= (3-5) / (5-(-2))
m= -2/7 ..........................(2)
The slope of CD :
m= (-1-3) / (2-5)
m= 4/3 ............................(3)
The slope of AD :
m= (-1-1) / (2-(-5))
m= -2/7 .............................(4)
Therefore,
The slope of AB is (1) 4/3, the slope of BC is (2) -2/7, the slope of CD is (3) 4/3, and the slope of AD is (4) -2/7.
Quadrilateral ABCD is a (5) parallelogram because (6) both pairs of opposite sides are parallel.
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4. building code does not permit building a house that is more than
35 feet tall. An architect working on the design shown at right would like
the roof to be sloped so that it rises 10 inches for each foot of horizontal
run.
(a) Given the other dimensions in the diagram, will the builder be allowed
to carry out his plan?
(b) Two vertical supports (shown dotted in the diagram) are to be placed
6 feet from the center of the building. How long should they be?
The builder will be able to execute his idea based on the other measurements in the illustration.
Explain about the inches?In the traditional system of measurement, one inch can be referred to as a unit of length. Inches of length are either denoted by in or by ". 5 inches, for instance, can be expressed as 16 inches or 16".
Initially, 1 inch was equal to the breadth of a man's thumb. In the 14th century, King Edward II of England decreed that 3 grains of barley laid end to end and lengthwise made up 1 inch.
Historically, there have been many different standards for what an inch is exactly, but since the international yard was adopted in the 1950s and 1960s, the inch has been based on the metric system and defined as precisely 25.4 mm.
Building codes prohibit the construction of homes that are taller than 35 feet.
The building is 22 feet tall in the diagram.
= 35 - 22
= 13 feet
so the builder is allowed to carry out is plan
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Hong runs 4 miles in 30 minutes. At the same rate, how many miles would he run in 48 minutes?
Answer: 6.4 miles
Step-by-step explanation:
Take 30 divided by 4 = 1 mile every 7.5 minutes
Then take 48 divided by 7.5 = 6.4 miles in 48 minutes
show your work
please
Answer:
C
Step-by-step explanation:
[tex]\frac{6y }{x^{8} } . \frac{4y}{x^{14} }\\\\\frac{24y^{2} }{x^{8+14} } \\\\\frac{24y^{2} }{x^{22} }[/tex]
Find the lengths of the hypotenuses (x) of the triangle whose legs are given
1) 9cm,12cm
Answer:
15 cm
Step-by-step explanation:
a² + b² = c²
(9 cm)² + (12 cm)² = c²
81 cm² + 144 cm² = c²
225 cm² = c²
c = √(225 cm²)
c = 15 cm
Answer: 15 cm
the ages for a random sample of 30 employees at house mart resulted in the following descriptive statistics. the lower and upper limits for a 99% confidence interval would be approximately and ?
The lower and the upper limit for a 99% confidence interval would be approximately 37.51 and 50.03
Here,
Mean = 43.77
Standard deviation (s)= 12.43655
n= 30
So,
CI= mean ± t (s/√n)
= 43.77±2.756(12.43655/√30)
= 43.77±6.26
= 37.51,50.03
So, the lower and upper limit would be 37.51 and 50.03
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What value of x is in the solution set of the inequality –2(3x 2) > –8x 6? –6 –5 5 6
The value of x in the solution set of the inequality -2(3x + 2) > -8x + 6 is 6.
Inequality is defined as relationship between non-equal numbers or expressions. The solution set of an inequality is the set of values that satisfies the given inequality.
To determine the solution set of the given inequality, isolate the variable to one side and simplify.
-2(3x + 2) > -8x + 6
-6x - 4 > -8x + 6
8x - 6x > 6 + 4
2x > 10
x > 5
x = (5, +∞)
Hence, the solution set of the given inequality is the set of numbers greater than 5. Among the given choices, only 6 is greater than 5. Therefore, the value of x is 6.
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Answer:
6
Step-by-step explanation:
edge on
What value of x is in the solution set of the inequality –2(3x + 2) > –8x + 6?
6
(4x)
(2x + 6)°
What is the value of x?
Answer:
8[tex]x^{2} \\[/tex] + 24x
Pls choose me as brainliest!
Enter the value of x below.
x+4=12
X=?
A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 80 patients. The sample mean was 1. 5 hours, with a sample standard deviation of 0. 7 hours. The upper- bound 95% confidence interval is.
In an effort to reduce wait times in the emergency room. Eighty patients were polled at random by the investigating committee. And, the upper-bound 95% confidence interval is found to be 1.64.
For small sample numbers or unidentified changes, the t-distribution is used in statistics to calculate the significance of population parameters.
Given sample mean [tex]\overline{X}[/tex] is 1.5 hours, sample size n is 80, and sample standard deviation s is 0.7 hours. Then, the standard error for the mean is,
[tex]\begin{aligned}SE_x&=\frac{s}{\sqrt{n}}\\&=\frac{0.7}{\sqrt{80}}\\&=0.07826\end{aligned}[/tex]
The degree of freedom is given by, df = n-1 = 80-1 = 79.
From the t-distribution table, [tex]t_{\alpha/2, 79}=1.7735[/tex]
Then, the upper-bound 95% confidence interval is calculated as,
[tex]\begin{aligned}\overline{X}+t_{\alpha,(n-1)}\frac{s}{\sqrt{n}}&\geq \mu\\&=\overline{X}+t_{0.08, 79}\frac{s}{\sqrt{n}}\\&=1.5+1.7735\left(\frac{0.7}{\sqrt{80}}\right)\\&=1.5+1.7735(0.07826)\\&=1.5+0.13879\\&=1.63879\\&\approx1.64\end{aligned}[/tex]
The required answer is 1.64.
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find the area enclosed by the curve x = t2 − 3t, y = t and the y-axis.
The area under the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].
Consider the following parametric equations:[tex]$$x=t^2-3 t \text { and } y=\sqrt{t} \text { and the } y \text {-axis. }$$[/tex]
The objective is to find area enclosed by the curve using the formula.
The area under the curve is given by parametric equations x=f(t), y=g(t), and is traversed once as t increases from α to β, then the formula for calculating the area under the curve:
[tex]$$A=\int_\alpha^\beta g(t) f^{\prime}(t) d t$$[/tex]
The curve has intersects with y-axis. so x=0
[tex]$$\begin{aligned}t^2-3 t & =0 \\t(t-3) & =0 \\t & =0 \text { or } t=3\end{aligned}$$[/tex]
Now we have to draw the graph,
Let f(t)=[tex]t^2-3 t, g(t)=\sqrt{t}$[/tex]
Differentiate the curve f(t) with respect to t.
[tex]f^{\prime}(t)=2 t-3[/tex]
Now, find the area under the curve use the above formula.
[tex]\begin{aligned}A & =\int_0^3(\sqrt{t})(2 t-3) d t \\& =\int_0^3(2 t \sqrt{t}-3 \sqrt{t}) d t \\& =\int_0^3\left(2 t^{\frac{3}{2}}-3 t^{\frac{1}{2}}\right) d t \\& =\left[2 \frac{t^{\frac{5}{2}}}{\frac{5}{2}}-3 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^3 \\& \left.\left.=\left[\frac{4 t^{\frac{5}{2}}}{5}-2 t^{\frac{3}{2}}\right]_0^3\right]^{\frac{5}{2}}\right] \\\\\end{aligned}$$[/tex]
[tex]& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right][/tex]
[tex]$\begin{aligned}& =\left[\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}\right]-\left[\frac{4(0)^{\frac{5}{2}}}{5}-2(0)^{\frac{3}{2}}\right] \\& =\frac{4(3)^{\frac{5}{2}}}{5}-2(3)^{\frac{3}{2}}-0 \\& =\frac{6 \sqrt{3}}{5}\end{aligned}[/tex]
Therefore, the area of the curve is [tex]\frac{6 \sqrt{3}}{5}[/tex].
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2.
What are the coordinates of the midpoint of the line
segment with endpoints (2,-5) and (8,3)?
1) (3,-4) 2) (3,-1) 3) (5,-4) 4) (5,-1)
Answer:
4) (5, -1)
Step-by-step explanation:
To find the midpoint, we must average the x coordinates to find the x-coordinate of the midpoint and average the y-coordinates to find the y-coordinate of the midpoint.
Thus, we do:
x-coordinate: [tex]\frac{2 + 8}{2}[/tex] = [tex]\frac{10}{2}[/tex] = [tex]5[/tex]
y-coordinate: [tex]\frac{-5 + 3}{2}[/tex] = [tex]\frac{-2}{2}[/tex] = [tex]-1[/tex]
This means the midpoint has an x-coordinate of 5 and a y-coordinate of -1. This can be expressed as the point (5, -1), which is option 4
Respond these question please
The percentile rank of the score 71 on the test is 26.7.
What is a percentile?The value that a specific percentage falls under is known as the percentile. Ben, for instance, is the fourth-tallest child in a group of 20, and eighty percent of the kids are shorter than you.
Given:
58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
Calculate the percentile of score 71 as shown below,
[tex]Percentile = n / N \times 100[/tex]
Here, n is the number of scores below 71 and N is the total number of scores,
Percentile = 4 / 15 × 100
Percentile = 0.267 × 100
Percentile = 26.7 percentile
Therefore, the percentile rank of the score 71 on the test is 26.7
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question 1: is the null hypothesis rejected or not rejected for an observed p-value of at 0.07 at a significance level of 0.05?
the null hypothesis is rejected for an observed p-value of at 0.07 at a significance level of 0.05.
At a significance level of 0.05, the p-value of 0.07 indicates that the observed value is not statistically significant. As a result, the null hypothesis cannot be disproven.In other words, the observed value is not strong enough to prove that the null hypothesis is false. Therefore, the null hypothesis is not rejected for an observed p-value of 0.07 at the significance level of 0.05.
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Find the values for each box using the image shown
Answer:
answer on the picture..........
Anyone Know f(-10)= 4.5,f(-2)=4.5??? Help ASAP
The linear function of f(-10)= 4.5,f(-2)=4.5 is y = 4.5.
How to represent linear function?Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the linear function of f(-10)= 4.5, f(-2)=4.5 can be represented as follows:
Using y = mx + b
4.5 = -10m + b
4.5 = -2m + b
b = 4.5 + 10m
Hence, using substitution,
4.5 = -2m + 4.5 + 10m
4.5 - 4.5 = 8m
m = 0
Let's find b
4.5 = -10(0) + b
b = 4.5
Therefore, the linear function is y = 4.5
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