The rate of change of the linear function represented by the table is 3
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The standard linear equation is in the form:
y = mx + b
Where m is the rate of change and b is the y intercept.
From the table, using the point (0, -7) and (2, -1):
m = [-1 - (-7)] / (2 - 0) = 3
The rate of change of the linear function represented by the table is 3
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a car travels 87 miles north and 114 miles west. what is the magnitude of the cars resultant vector
The magnitude of the resultant vector is 27 miles
How to determine the vector magnitudeResultant vector = Distance of A - Distance of B
This is so because of the opposite direction of the car's movement
A = 87 miles
B = 114 miles
Resultant vector = 114 - 87
Resultant vector = 27 miles
Thus, the magnitude of the resultant vector is 27 miles
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Given: p: x is prime. q: x is even. What is the truth value of p^q when x is replaced by 2?
Truth Value for p^ q when x is replaced by 2 is also true. ( p^q is True)
What is a prime number?The prime numbers are those numbers that have only one factor namely 1 and the number itself.
Given that p = x is prime and q = x is even. If we replace x by 2 then we would get
p = 2 is prime
q = 2 is even
p^q will be held true only if p and q both are true.
The statement for p and q both are true because 2 only has two factors only 1 and 2 themselves.
2 is also considered an even number (2,4,6,8,...)
Since p = true and q = true then
p and q = p^q = true
Thus, p^q is True.
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Answer:
p^q is true
Step-by-step explanation:
If both p and q are true, the statement p^q is true. If both p and q are false, the statement p^q is still true. All other options yield a false result.
5. Given (x + 1) and (x-3) are factors of P(x) = x4-5x³-7x² + cx + d. Determine the values
of the constants c and d.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
How to determine the missing coefficients of a quartic equation
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of linear equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
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You are looking at a map of the united states, and it is assumed that you already know which direction is north
When one is looking at a map of the united states, and it is assumed that you already know which direction is north, this illustrates a theorem.
What is a theorem?It should be noted that a theorem simply means a statement that has been proved.
In this case, when one is looking at a map of the United States, and it is assumed that you already know which direction is north, this illustrates a theorem. This is because it's proven.
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soybeans have a conversion factor of 36.744 (bu/t). how much do 45 bushels weight. Show your work pls
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
How many tonnes are a given quantity of bushels?
In this question we have an application of direct proportionality model, whose form is shown below:
y = k · x (1)
Where:
x - Quantity of bushelsk - Conversion rate, in tonnes per bushel.y - Quantity of tonnesIf we know that x = 45 bu and k = 1/36.744, then the soybean quantity in tonnes is:
y = (1/36.744 t/bu) · (45 bu)
y = 1.225 t
By using unit conversion and direct proportionality model, we find that 45 bushels of soybeans are equal to a weight of 1.225 tonnes.
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You have a bag of marbles that has 12 red, 5 green, 6 yellow, and 4 blue. If you draw one at random. what is P(red)? (What would the percent of choosing red be)
[tex]|\Omega|=12+5+6+4=27\\|A|=12\\\\P(A)=\dfrac{12}{27}=\dfrac{4}{9}=44.4\%[/tex]
Answer: 44.44% approximately
Work Shown:
P(red) = (number of red)/(number total)
P(red) = (12 red)/(12 red + 5 green + 6 yellow + 4 blue)
P(red) = (12 red)/(27 total)
P(red) = 12/27
P(red) = 4/9
P(red) = 0.4444 approximately
P(red) = 44.44% approximately
Angela is starting a new business, selling shirts and dresses that she sews herself, The materials for the skirts cost 13.56 and the materials for the dresses cost 18.79. She only has $80 to spend. She still has a regular job, so she is limited on the time she has to sew her products. She only wants to spend 15 hours sewing; it takes 2 hours to sew a skirt, and 4 hours to sew a dress
The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP3 player was sold at the regular price. Reported below is the number of units sold last month at the regular and reduced prices at the randomly selected outlets. Regular price 138 124 89 112 116 123 98 Reduced price 124 134 154 135 118 126 133 132 i. Compute the pooled estimate of the variance. (Round your answer to 3 decimal places.)
ii. Compute the test statistic. (Round your answer to 2 decimal places.)
iii. State your decision about the null hypothesis.
The pooled estimate of the variance is 187.650 and the test statistic is -2.32
Pooled estimate of the varianceThe dataset is given as:
Regular price 138 124 89 112 116 123 98
Reduced price 124 134 154 135 118 126 133 132
Let the regular price be dataset 1 and the reduced price be dataset 2.
So, we have:
#1: 138 124 89 112 116 123 98
#2: 124 134 154 135 118 126 133 132
Calculate the sample means and the sample standard deviations using a graphing calculator.
#1
[tex]\sigma_1 = 16.56[/tex]
[tex]\bar x_1 = 114.29[/tex]
[tex]\sigma_1^2 = 274.24[/tex]
#2
[tex]\sigma_2 = 10.65[/tex]
[tex]\bar x_2 = 132[/tex]
[tex]\sigma_2^2 = 113.43[/tex]
The pooled estimate of the variance is:
[tex]\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}[/tex]
This gives
[tex]\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}[/tex]
Evaluate the factors
[tex]\sigma_p^2 = \frac{2439.45}{13}[/tex]
Divide
[tex]\sigma_p^2 = 187.65[/tex]
Hence, the pooled estimate of the variance is 187.650
The test statisticThis is calculated using:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}[/tex]
This gives
[tex]t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}[/tex]
This gives
[tex]t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}[/tex]
Evaluate the product
[tex]t = \frac{-17.71}{\sqrt{58.08214}}[/tex]
Evaluate the exponent
[tex]t = \frac{-17.71}{7.62}[/tex]
Divide
t = -2.32
Hence, the test statistic is -2.32
The decision about the null hypothesisThe critical value at 0.025 significance level is -1.96
-2.32 is less than -1.96
This means that we accept the null hypothesis
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If a/(b+c+d)=4/3 and a/(b+c)=3/5, find the value of d/a
Answer:
I did this quickly, so please check carefully.
d/a = -(11/12)
Step-by-step explanation:
a/(b+c+d)=4/3
3a = 4(b+c+d) [Cross multiply]
3a = 4((b+c)+d) [Note that b and c can be grouped as (b+c)]
---------------------
We can see the second equation also has a (b+c) group. Isolate it to one side:
a/(b+c)=3/5
5a = 3(b+c)
(b+c) = (5a/3)
------------------
Now use this definition of (b+c) in the first equation:
3a = 4((b+c)+d)
3a = 4((5a/3)+d) [Use the new value of (b+c), which is (5a/3)]
3a = 4(5a/3+3d/3)
3a = 4((5a + 3d)/3)
3a = (4/3)(5a + 3d)
3a = (20/3)a + 4d
9/3a = (20/3)a + 4d
-(11/3)a = 4d
4d = -(11/3)a
d = -(11/12)a
d/a = -(11/12)
2 six-sided dice, one colored green and one red, are released. Find the probability that : either the score on the green die is 1, or the score on the red die is 6, but not both.
The probability that either the score on the green die is 1 or the score on the red die is 6, but not both, is 11/36.
To find the probability that either the score on the green die is 1 or the score on the red die is 6 (but not both), we can break it down into two mutually exclusive events and then calculate their probabilities separately.
Event A: The score on the green die is 1.
Event B: The score on the red die is 6.
We need to find the probability of either event A or event B occurring but not both.
The probability of event A occurring is the probability of rolling a 1 on the green die.
Since each die is six-sided, the probability of rolling a 1 on the green die is 1/6.
The probability of event B occurring is the probability of rolling a 6 on the red die. Similarly, the probability of rolling a 6 on the red die is 1/6.
To calculate the probability of either event A or event B occurring but not both, we need to subtract the probability of both events occurring simultaneously from the sum of their individual probabilities.
The probability of both event A and event B occurring simultaneously is the product of their individual probabilities, which is (1/6) x (1/6) = 1/36.
So, the probability of either event A or event B occurring but not both is:
Probability = (Probability of event A) + (Probability of event B) - (Probability of both events occurring)
= (1/6) + (1/6) - (1/36)
= 6/36 + 6/36 - 1/36
= 11/36
Therefore, the probability is 11/36.
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pls help asap.........
11. The value of x is [tex]13\frac{3}{4}[/tex]
12. From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x
Linear equationsFrom the question, we are to solve the given equation
The given equation is
[tex]5 + \frac{1}{2}(4x +5) = 35[/tex]
This becomes
[tex]\frac{1}{2}(4x +5) = 35-5[/tex]
[tex]\frac{1}{2}(4x +5) = 30[/tex]
[tex]4x +5 = 2 \times 30[/tex]
[tex]4x +5 = 60\\[/tex]
[tex]4x= 60-5[/tex]
[tex]4x= 55[/tex]
[tex]x = \frac{55}{4}[/tex]
[tex]x = 13\frac{3}{4}[/tex]
Hence, the value of x is [tex]13\frac{3}{4}[/tex]
12.
From given to step 1, Iquolese should have combined like terms on each side of the equation to get 3x + 11 = 101 + x
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HELP ME ASAP PLEASE
A statistics student is taking a poll of his high school classmates and their senior prom
preferences. He asks those polled, "Last year tickets for the senior prom were $60 each.
This year tickets will need to be $70 if we have a live band perform. Would you like to see
a live band perform at this year's senior prom?" Is this a valid question?
According to the information, it can be inferred that the answer is No, because informing the students that there will be a $10 increase... (option B).
Why is this question invalid?This question is not valid because it specifies information that would surely change the answer of the respondent.
The information that the question reveals is that there is going to be a raise, this will cause a refusal in people to accept that raise just to see a live band.
According to the above, the question is invalid because it reveals information that will modify the answer of those who respond.
Note: This question is incomplete because the options are missing. Here are the options:
A. No, because questions about musical preferences are always invalid because you cannot measure people's opinions on subjective manners like music and other creative arts.
B. No, because informing the students that there will be a $10 increase in the cost of a prom ticket may make them more likely to say that they would not like a live band to perform.
C. No, because students should be given a sample of the band's music to allow them to offer a more informed opinion.
D. No, because a random sample of all seniors in the country should have been taken to determine if a live band should perform at this high school's senior prom.
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Oak street and elm street run parallel to each other when Main Street intersects them it forms interior <6 measuring70 what is the measure of <4
IfIf it forms interior <6 measuring70. The measure of <4 is: B. 110°.
Measure of <4Using this interior angle theorem
Measure of <4=180° - <6
Where:
<6 measure 70
Hence:
Measure of <4=180°-70°
Measure of <4=110°
Therefore the measure of <4 is: B. 110°.
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Please help! Billy just received $10 for his birthday and immediately spent $2.50 on a pack of baseball cards. He then wants to buy some boxes of candy that cost $1.50 each.
If Billy has $7.50 remaining, which of the following equations will give you the number of boxes, x, that Billy could buy?
Answer:
1.5x = 7.5 (a)
Step-by-step explanation:
If Billy has $7.50 remaining, then he can buy x no. of boxes.
Each box costs $1.50
So, 1.5x = 7.5
6x+7=-5 i got it wrong
Answer:
x = -2
Step-by-step explanation:
Subtract 7 from both sides :
6x = -12
Divide both sides by 6 :
x = -2
Hope this helped and have a good day
Madeline uses a mirror on the ground to measure the height of her school building. She walks a distance of 9.5 m from the building, then place is a mirror flat on the ground. she then walks 2.75 more meters
The height of the building is 5.33m.
How to calculate the height?The question is to calculate the height of the building.
Based on the information given, the height will be:
Madeline eye height/Distance from X = Height of building/Building distance from X
1.55/2.75 = x/9.45
x = (1.55 × 9.45)/2.75
x = 5.33 m
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Solve the following....
4(5-2x)+3=7
Answer:
x = 2
Step-by-step explanation:
1) If there is a number right next to a bracket, then it means that it should be multiplied. --> 4(5 -2x) = 25 - 10x
2) (20 - 8x) + 3 = 23 - 8x
3) 23 - 8x = 7
4) 16 = 8x
5) We divide both sides with 8 to leave x. --> 2 = x
6) x = 2
Baby rabbits were sorted into three groups, based upon which food they preferred when given a choice: Brand A rabbit food, Brand B rabbit food, or a diet of raw vegetables. For two months each group was restricted to their preferred diet (they were no longer given a choice in diet). Measurements for the height, weight, and length of the rabbits was taken each week for two months. The rabbits in the group with the diet of raw vegetables had significantly more growth that the other two groups. What conclusion can be drawn from this study?
Answer: That raw vegetables are better for the rabbit's growth than rabbit food.
Answer:
The rabbit food that was strictly a diet of raw vegetables is healthier for the rabbits.
Step-by-step explanation:
Y=
Help me please thank you
Answer:
-135689;456+((888888888
Do exponent laws apply all the time when simplifying variables?
It is true that exponent laws apply all the time when simplifying variables
How to determine the true statement?The laws of exponent state that:
[tex](ab)^m = a^m * b^m[/tex]
[tex](a+ b)^m \ne a^m + b^m[/tex]
[tex](a- b)^m \ne a^m - b^m[/tex]
[tex](a/b)^m \ne a^m / b^m[/tex]
The above laws must be followed in all variables.
When any of the law is misinterpreted, misrepresented or misused in simplifying variables, the result would be incorrect
Hence, it is true that exponent laws apply all the time when simplifying variables
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Will give brainliest and about 45 points
Answer:
[tex]\sf C. - \dfrac{3}{4}[/tex]
Explanation:
[tex]\sf Given \ equation : 4x - 3y = 12[/tex]
Rewrite in slope intercept form "y = mx + b"
[tex]\rightarrow \sf 4x - 3y = 12[/tex]
[tex]\rightarrow \sf - 3y = 12 - 4x[/tex]
[tex]\rightarrow \sf y =\dfrac{ 12 - 4x}{-3}[/tex]
[tex]\rightarrow \sf y =\dfrac{ 4}{3}x - 4[/tex]
Here the slope is 4/3 and y-intercept is -4
Perpendicular lines has negatively inverse slope.
→ per. slope = -(slope)⁻¹ = -(4/3)⁻¹ = -3/4
Answer:
[tex]-\dfrac{3}{4}[/tex]
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y=mx+b[/tex]
where:
m is the slopeb is the y-interceptGiven linear equation:
[tex]4x-3y=12[/tex]
Find the slope of the given linear equation by rewriting the equation so that it is in slope-intercept form (i.e. make y the subject):
[tex]\implies 4x-3y=12[/tex]
[tex]\implies 4x-3y+3y=12+3y[/tex]
[tex]\implies 4x=12+3y[/tex]
[tex]\implies 4x-12=12+3y-12[/tex]
[tex]\implies 4x-12=3y[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{4}{3}x-\dfrac{12}{3}[/tex]
[tex]\implies y=\dfrac{4}{3}x-4[/tex]
Therefore, the slope of the given line is 4/3.
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to the given line is:
[tex]\implies m \times \dfrac{4}{3}=-1[/tex]
[tex]\implies m=-\dfrac{3}{4}[/tex]
If -8. min 19 are in an AP, find the values of m and n
Answer:
m = 1 and n = 10.
Step-by-step explanation:
I am assuming you mean -8, m , n, 19.
If they are in AP the 4 terms will have a common difference.
19 - (-8) = 19 + 8 = 27.
So the increase over 3 terms (from -8 to 19) is 27 so we have:
27 / 3 = 9
Therefore the common difference is 9 and the A P is
-8, 1, 10, 19.
Im so confused please help me :((
Answer:
[tex]A) \sf \ \sf \dfrac{x^8}{16y^4}[/tex]
Explanation:
[tex]\sf \left(\dfrac{2y}{x^2}\right)^{-4}[/tex]
inverse of the expression
[tex]\sf \left(\dfrac{x^2}{2y}\right)^{4}[/tex]
distribute power inside parenthesis
[tex]\sf \left(\dfrac{(x^2)^4}{(2y)^4}\right)[/tex]
apply exponent rules: [tex]\s(a^b )^c = a^{bc}[/tex]
[tex]\sf \dfrac{x^8}{16y^4}[/tex]
someone solve this plsss
. Expand: 31og2 (9n)
By definition of logarithm the value of [tex]$3log _2(9n)[/tex] exists
[tex]$ 6(log _2(3) +3 log _2(n))[/tex].
What is a logarithm?A logarithm exists as an amount that conveys power to a specified number contains to be raised to create the assigned number.
From the definition of a logarithm, we get
aˣ = b exists the same as x = logₐb
Given: [tex]$3log _2(9n)[/tex]
Simplifying [tex]$log _2(9n) = 2log _2(3) + log _2(n)[/tex]
[tex]$= 3(2log _2(3) + log _2(n))[/tex]
Expanding the equation, we get
[tex]$3(2log _2(3) + log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
[tex]$= 6(log _2(3) +3 log _2(n))[/tex]
Therefore, the value of [tex]$3log _2(9n)[/tex] exists [tex]$ 6(log _2(3) +3 log _2(n))[/tex].
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How does this graph change between point D and point G?
A graph increases from point D to point G, and then decreases.
The graph increases.
The graph decreases.
The graph increases, then decreases.
The graph remains constant.
Answer:
The graph increases.
Step-by-step explanation:
hope this helps!!
Answer: the graph increases
Step-by-step explanation: did test
You and two friends plan to walk your dogs together. You want the meeting place to be the same distance from each person’s residence. Explain how you can use the diagram to locate the meeting place.
A company has 12 000 employees. During the financial crisis in 2008, 2.5 % of them were retrenched
50.75 % of them had a pay cut and the rest were unaffected. Find the number of employees who
were unaffected by the financial crisis.
Answer:
5610
Step-by-step explanation:
unaffected people will be (100%-2.5\%-50.75%)=46.75% of 12000:
[tex]12000\cdot 46.75\%=12000\cdot \frac{46.75}{100} =120\cdot 46.75=5610[/tex]
Lacey has $36 to spend. She buys a pair of sunglasses for $14.89 and a hat for $9.33. Lacey buys a scarf with the remaining money. How much does Lacey spend buying a scarf?
Answer:
$11.78
Step-by-step explanation:
14.89+9.33=24.22
36-24.22=11.78
The question is on the picture
Answer: 68
Step-by-step explanation:
By the inscribed angle theorem, arc BA measures twice of 34 degrees, which is 68 degrees.