The p-value is higher than 0.05, so we are unable to rule out the null hypothesis. There is little proof to back up the director's claim.
Hypothesis:
H₀ : μ = 3000
H₁ : μ > 3000
The t-test should be employed when the population mean and standard deviation are unknown. Since the sample size is high, we can infer that the sample mean's sampling distribution is normal.
The following information is provided:
s = 450
x = 3200
n = 14
Therefore, test statistics will be:
t = (x - μ) / (s / √n) = (3200 - 3000) / (250 / √14) = 1.66
The test in this instance is right-tailed, and its degree of freedom is df=n-1=14-1=13.
0.0601 is the p-value.
We are unable to reject the null hypothesis since the p-value is higher than 0.05. The director's allegation is not supported by a lot of evidence.
Since p =.0601, the director's assertion cannot be supported by the available data.
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a man 6 ft tall walks at the rate of 5 ftsec toward a streetlight that is 16 ft above the ground. at what rate is the length of his shadow changing when he is 10 ft from the base of the light?
The rate at which length of shadow of person changing is 3 ft /sec.
What is meant by time rate?The literal formula for the relationship between distance, rate, and time is distance=rate×time=rtH = Height of streetlight; 16 ft
h = Height of man; 6 ft
x = Length of man's shadow.
s = Distance from streetlight to man.
Using the similarities of the triangles.
H/h = (s + x)/x
Hx = h(s + x)
Differentiate with respect to 't' on both sides.
H(dx/dt) = h(ds/dt + dx/dt)
Put the values.
16(dx/dt) = 6(5 + dx/dt)
16(dx/dt) = 30 + 5dx/dt
10dx/dt = 30
dx/dt = 3 ft /sec
Thus, the rate at which length of shadow of person changing is 3 ft /sec.
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What is the domain of the following function
The domain of the given function is equal to: {-4, 2, 6, 9}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values or numbers to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Generally speaking, the horizontal extent of the graph of a function represents all domain values and they are read and written from the smallest to the largest numerical values, and from the left of a graph to the right.
By critically observing the given function, we can reasonably and logically deduce the following:
Domain = {-4, 2, 6, 9}.
Range = (-3, 1).
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Find the value of x if 3x = 23² – 17²
Answer:
The answer is 80
state: how heavy a load (in pounds) is needed to pull apart pieces of douglas fir 4 inches long and 1.5 inches square? data from students doing a laboratory exercise are given.
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
Define confidence interval.In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. The size of a 90% confidence interval for a given estimate is one way to gauge how "excellent" it is; the greater the interval, the more care must be used when utilizing the estimate. Confidence intervals serve as a crucial reminder of the estimates' limits.
Given,
Data set: (33190, 31860, 32590, 26520, 33280, 32320, 33020, 32030, 30460, 32700, 23040, 30930, 32720, 33650, 32340, 24050, 30170, 28730, 31920)
The normal distribution's standard deviation, s = 3000 pounds
95% confidence interval
N = 20 observations were made.
Mean = 30,800
Margin of error :
z₇ × √3000².20
±1.314.8079
Confidence interval
= Mean + Margin of error
= 30,800 ±1.314.8079
= 29,485.192 , 32,114.8
The range of the confidence interval for the mean load needed to separate the wood is (29,485.192 , 32,114.8).
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HELP ASAP!!! THANK YOU
To balanced hanger, adding a circle to the left and a square to the right. To both sides, add two triangles. The option 1, 2, and 5 are correct.
What is balanced hanger?
Because each side of the hanger is evenly spaced from the center and has a same amount of overall weight, they are balanced against one another. During the warm-up, students come across two real hangers—one is balanced and the other is slanted—and they observe and consider what might have caused the hangers' appearance.Adding two circles to the left side and a square to the right would adjust the hanger's balance in accordance with the lesson's emphasis on maintaining the equation in balance.
adding a circle to the left and a square to the right. To both sides, add two triangles.
Hence the option 1, 2, and 5 are correct.
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PLEASE HELP ME EASY 8TH GRADE MATH!!!!
Answer: The probability is 3 out of 20
Step-by-step explanation:
Base of an isosceles triangle can be right angles
We can actually deduce here that the statement, "base of an isosceles triangle can be right angles" is false.
What is an isosceles triangle?An isosceles triangle is actually known to be a triangle which has two sides equal and opposite angles of the sides also equal. In other words, an isosceles triangle must have at least two equal triangles.
Some of the properties of an isosceles triangle are:
It is a triangle whose two sides are congruent to each otherIt has a third side known as the base of the isosceles triangle.It has angles that are opposite to the equal sides which are congruent to each other.We see here that the base of an isosceles triangle cannot be a right angles. It is still to have one side as a right angle but not the two sides as right angles.
The complete question is:
True or false: Base angles of an isosceles triangle can be right angles.
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Set up the form for the partial fraction decomposition. Do not solve for A, B, C, and so on.
Answer:
For part a you would decompose the fraction into two independent fractions with the following form:
() = ()/( x^2+5)(x ^2+3x−4) = (Ax + B)/(x^2+5) + (Cx + D)/(x ^2+3x−4)
Combining these fractions we get:
((Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5))/( x^2+5)(x ^2+3x−4) = ()/( x^2+5)(x ^2+3x−4)
Thus we can say: (Ax + B)*(x ^2+3x−4) + (Cx + D)*( x^2+5) = ()
You then simplify the equation on the left by combining like terms and solve the system of equations that arise corresponding with ().
You would follow a similar process for part b as well.
Step-by-step explanation:
What integers are the solutions to
|x-4| < 8 and |-3x| > 12
Answer:
x-4<12 x<-4
-3x<12
-3x/-3=x
12/-3=-4
x-4+4=x
8+4=12
An element with a mass of 420 grams decays by 7.5% per minute. To the
nearest minute, how long will it be until there are 210 grams of the element
remaining?
Answer: x= 9
Step-by-step explanation:
I just checked that its right!
Answer:
The correct answer would be 9
Step-by-step explanation:
help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Write an equation in standard form with an x-intercept of 4 and a y-intercept of 5.
Equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
Given:
x - intercept = 4
y - intercept = 5
At x intercept y = 0 and at y intercept x = 0
(4,0) and (0,5)
slope = 5-0/0-4
= 5/-4
m = -5/4
substitute (4,0) and m value,
y = mx+c
0 = -5/4*4 +c
0 = -5 + c
c = 5
y = mx + c
y = -5/4(x) + 5.
Therefore equation in standard form with an x-intercept of 4 and a y-intercept of 5 is y = -5/4(x) + 5.
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Solve the equation given a domain of {-3}.
3x - 2y = 5
Solution of the equation 3x-2y = 5 for domain {-3} is (-3,-7).
Given,
Eq => 3x - 2y = 5
Domain = x = -3
Put x = -3 in equation
3(-3) - 2y = 5
-9 - 2y = 5
-9 - 5 = 2y
-14 = 2y
y = - 14 / 2
= -7
Hence, solution is (-3,-7).
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What is the slope of the line that passes through the points (-6, -6) and (-9, -5)? Write your answer in the simplest form.
Answer: -1/3
Step-by-step explanation:
The formula for slope =y1-y2/x1-x2. You first subtract the numbers for the y coordinate which is -6-(-5), and thats -1. Then you subtract the x coordinates. -6-(-9)=3. So the slope is -1/3
evaluate the expression 2x^3 - 14 when x=2
Answer:
-2
Step-by-step explanation:
2(2)*3-14
4*3-14
12-14
-2
Determine the algebraic rule to describe the relationship between x and y. Give your answer in the form y = mx + c Total: [10] Please draw a line before you start with the next question.
Eplaination of algebraic rules with equation of line is describe below
What is algebraic rules ?Algebraic rules are maths expression of two variable that can be written in the form of equation.
Now we will understand by the equation of line given in the question,
we have Y = mx + c
where y is the intercept on y-axis, m is the slope of line, x is intercept on x-axis, and c is the point where line cuts y-axis.
This equation represent the line which follows algebraic rules.
Graph of equation:
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T2 Midterm Re
1. X and Y are two fractions. X is greater than 0 but less than 1.
Which statement describes the product of X and Y?
A.
The product is less than -1.
B. The product is greater than -1 but less than 0.
C. The product is greater than 0 but less than 1.
D. The product is greater than 1.
Answer: The correct answer is C. The product is greater than 0 but less than 1.
Step-by-step explanation:
X and Y are both fractions
X is greater than 0 but less than 1
X * Y > 0 and < 1
The product of these two fractions will result in a fraction between 0 and 1.
For example:
1/2 x 1/2 =1/4, 1/6 x 2/6 = 1/18, 1/10 x 5/6 = 1/12
write an equation of the line in slope intercept form
The equation of the line in slope intercept form is y = (-4/3)x .
In the question ,
a line graph is given ,
we need to find the equation of that line .
the two points that are given on the line graph are (-3 , 4) and (0 , 0) ,
the equation of the line passing from the points (x₁ , y₁) with slope m in the slope intercept form is given by
(y - y₁) = m(x - x₁) .
we first need to find the slope .
So , m = (0 - 4)/(0 + 3)
m = -4/3
The equation of the line passing from the points (-3 , 4) with slope -4/3 , in the slope intercept form is
(y - 4) = (-4/3)(x -(-3))
y - 4 = (-4/3)(x + 3)
y - 4 = (-4/3)x - 4
y = (-4/3)x - 4 + 4
y = (-4/3)x
Therefore , The equation of the line in slope intercept form is y = (-4/3)x .
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A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
The amount of money paid by each of the 4 persons will be $33.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.
Total cost = $105.73 x 1.06 x 120
Total cost = $134.48
Amount for each person,
A = $134.48 / 4
Amount = $33.62
Therefore, the amount of money paid by each of the 4 persons will be $33.6.
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please help look at picture
Can someone please help me
Please help thank you
By comparing the fractions of rocks that skip over the poind for Jessica and Henry, we will see that Jessica gets more rocks to skip over the pond.
Who gets more rocks to skip over the pond?We know that for every 9 rocks that Herny throws, 5 skip over the pond. Then the fraction for Henry is:
H = 5/9
While for Jessica we know that for every 12 that she throws, 7 skip over the pond, so her fraction is:
J = 7/12
Now we only need to see which one of the fractions is larger.
If we simplify both we will get:
H = 5/9 = 0.556
J = 7/12 = 0.583
So we can see that Jessica's fraction is larger, which means that she will get more rocks.
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Solve the inequality. x² + 4x - 21 ≥ 0
and please explain
Step-by-step explanation:
if the solution has "nice" numbers, we can split the expression into 2 factors in the form
(x + a)(x + b) = x² + (a+b)x + ab
as this is equal to x² + 4x - 21.
ab = -21
so, one is positive and one is negative.
and 4 = a + b
we know the typical factors of 21 : 3×7
and then we see easily : 7-3 = 4
so,
we have
(x + 7)(x - 3) >= 0
this has 2 x-intercepts (x-values when y = 0) :
x = -7
x = 3
because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.
that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.
so, the solution are the intervals
x <= -7 and x >= 3
in these areas is the expression x² + 4x - 21 >= 0.
Which of the following statements about the box-and-whisker plot below is true?
10 20 30
40
70 80 90 100 110 120 130 140 150
There are more data points in the upper two quartiles than in the lower two quartiles.
There are more data points inside the data box than are in the outside the data box.
The midrange of the data set shown is 85.
The midrange of the data set shown is 55.
50 60
The midrange of the data set shown is 85 is true about the box-and-whisker plot below. The middle is the number in question. The least and greatest values should be added together, divided by two, or, in other words, the mean of the least and biggest values should be determined.
How do you find the midrange on a box and whisker plot?It is also helpful to know the number that lies halfway between the data set's lowest and highest values. The middle is the number in question. The least and greatest values should be added together, divided by two, or, in other words, the mean of the least and biggest values should be determined.so,The midrange of the data set shown is 85midrange: Divide by two the sum of the highest and lowest values. 125 is the range. The middle number is 82.5.The difference between the greatest and smallest numbers called the range. The midpoint represents the mean between the largest and lowest number.To learn more about midrange refer to:
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Find the least common multiple of the given algebraic terms. x², 2xy, 3y
Step-by-step explanation:
common factor= x and y
remaining factor = x , 2 , 3
L.C.M = 6 x sq. y
i,d like to order 7 halves for my family plus i want some extra for y 6 friends they'll each want a quarter whats the answer
The total number of cupcakes ordered, using proportions, is of:
5.
What is a proportion?A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem to find the desired amounts in the same context of the problem.
These amounts are found using basic arithmetic operations, especially multiplication and division, with the unit rates in the context of the problem.
In this problem, the amounts are given as follows:
Family: Seven halves of cupcakes = 7/2 = 3.5 cupcakes.Friends: Six quarters of cupcakes = 6/4 = 1.5 cupcakes.The total number of cupcakes that will be ordered is the sum of the amounts that will be needed for the family and for the friends, hence:
3.5 cupcakes + 1.5 cupcakes = 5 cupcakes.
Missing InformationThe problem is:
I'd like to order 7 halves of cupcakes for my family plus an amount for six friends, considering that each of them wants a quarter. What is the total amount?
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SOLVE FOR X answer .
Answer:
31
Step-by-step explanation:
x+10+2x+20+2x-5=180
5x+25=180
5x=155
x=31
I need help I don’t understand how it’s wrong
==========================================
Explanation:
If it is possible to draw a single vertical line through more than one point on the blue graph, then that graph is not a function. We consider it failing the vertical line test. Such a thing happens in the middle of the top row (graph 2). A vertical line intersects the sideways parabola at more than one point.
Recall a function is when any given input leads to exactly one output. We can't have the input x = 4 lead to both y = 1 and y = -3 at the same time for instance.
Graph 4 is another instance where we don't have a function for similar reasoning. This graph fails the vertical line test. So does graph 6.
The other graphs (1, 3, and 5) all pass the vertical line test since it's not possible to draw a single vertical line to intersect through more than one blue point.
a catering company needs 8.75 lb of shrimp for a small party. they buy lb of jumbo shrimp,3 2 3 lb of medium-sized shrimp, and some mini-shrimp. how many pounds of mini-shrimp do they2 5 8 buy?
Finally, we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
Given that;
A catering company needs 8.75 lbs of shrimp for a small party. they buy [tex]3\frac{2}{3}[/tex] lbs of jumbo shrimps, [tex]2\frac{5}{8}[/tex] lbs of medium-sized shrimps, and some mini-shrimps.
The total of 8.75th is changed as [tex]8\frac{3}{4}th\\[/tex]
Sum of [tex]3\frac{2}{3}[/tex] + [tex]2\frac{5}{8}[/tex] this is bought by the company.
So, to purchase the remaining [tex]8\frac{3}{4}th\\[/tex] - [tex]3\frac{2}{3}[/tex] - [tex]2\frac{5}{8}[/tex]
We use a common denominator of 24 for the fraction parts.
Change [tex]8\frac{3}{4}[/tex] as [tex]8\frac{18}{24}[/tex]
Similarly, convert;
[tex]3\frac{2}{3}[/tex] as [tex]3\frac{16}{24}[/tex]
[tex]2\frac{5}{8}[/tex] as [tex]2\frac{15}{24}[/tex]
By solving all the above conversions, we get;
[tex]\frac{42-16-15}{24}[/tex] = 11/24
Considering all the factors together we have [tex]2\frac{11}{24}[/tex] lbs of mini shrimps.
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please help me out on this ASAP!!
The value of k for which the quadratic equation 4s² - 4s + (k - 2) has one real solution is:
k = 16.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by the rule presented as follows:
y = ax² + bx + c
The discriminant of the quadratic function is given as follows:
Δ = b² - 4ac.
The numeric value of the coefficient and the number of solutions of the quadratic equation is defined as follows:
Δ > 0: two real solutions.Δ = 0: one real solution.Δ < 0: two complex solutions.In this problem, the equation is given as follows:
4x² - 4s + (k - 2) = 0.
Hence the coefficients are given as follows:
a = 4, b = -4, c = k - 2.
Hence the discriminant is:
Δ = (-4)² - 4(4)(k - 2)
Δ = 16 - 16k + 32
Δ = 48 - 3k
It has one real solution if Δ = 0, hence:
48 - 3k = 0
3k = 48
k = 48/3
k = 16.
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