Answer:
112.5
Step-by-step explanation:
To find the area of a parallelogram, you can simply multiply the length of the base by the height. In this case, this is 15*7.5=112.5 square centimeters. Hope this helps!
Answer:
Step-by-step explanation:
the sum of three consecutive numbers is 114 . what is the smallest of these numbers
Answer:
x + (x+1) + (x+2) = 114
3x = 111
x = 37
the numbers are 37, 38 and 39
the smallest number is 37
Step-by-step explanation:
Solve the inequality
Math question
Answer:
AAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
x < 7
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Answer:
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And the confidence interval is given by:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] \bar X_1 = 186[/tex] the sample mean for the first sample
[tex] \bar X_2 = 171[/tex] the sample mean for the second sample
[tex]s_1 =33[/tex] the sample deviation for the first sample
[tex]s_2 =23[/tex] the sample deviation for the second sample
[tex]n_1 = 8[/tex] the sample size for the first group
[tex]n_2 = 7[/tex] the sample size for the second group
The confidence interval for the true difference is given by:
[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]
We can find the degrees of freedom are given:
[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]
The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:
[tex] t_{\alpha/2}= \pm 1.77[/tex]
The point of estimate for the true difference would be:
[tex] 186-171= 15[/tex]
And replacing into the formula for the confidence interval we got:
[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]
[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]
Solve the system of equations using the elimination method 4x+5y=40 6x+3y=42
Answer:
The solutions to the system of equations are [tex]y=4,\:x=5[/tex].
Step-by-step explanation:
To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]
First,
[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]
[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]
Subtract the first equation from the second equation
[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]
Solve [tex]-9y=-36[/tex] for y:
[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]
For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x
[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]
The solutions to the system of equations are:
[tex]y=4,\:x=5[/tex]
The tuition at a college was $30,000 in 2012, $31,200 in 2013, and $32,448 in 2014. The tuition has been increasing by the same percentage since the year 2000.
The equation C(T) = LaTeX: 30000\cdot1.04^T
30000
⋅
1.04
T
represents the cost of tuition, in dollars, as a function of T, the number of years since 2012. Explain what the 30,000 and 1.04 tell us about this situation.
What is the percent increase in tuition from year to year?
What does C(3) mean in this situation? Find its value and show your reasoning.
a. Write an expression to represent the cost of tuition in 2007.
b. How much did tuition cost that year?
Previous Next
The meaning of each parameter is given as follows:
30,000: cost in the reference year of 2012.1.04: rate of change.Then the yearly percent increase is of:
4%.
C(3) represents the cost in 2015, which was of $33,746.
a) The expression to represent the cost in 2007 is of: C(-5).
b) The cost was of: $24,658.
How to define an exponential function?An exponential function is defined as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.For this problem, the function is defined as follows:
y = 30000(1.04)^x.
In which:
x is the number of years since 2012.y is the cost in x years after 2012.C(3) represents the cost in 2015 and is obtained as follows:
C(3) = 30000(1.04)^3 = $33,746.
C(-5) represents the cost in 2007 and is obtained as follows:
C(-5) = 30000(1.04)^(-5) = $24,658.
(as 2007 was five years before 2012).
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Triangles BAD and BDC are right triangles with AB = 12 units, BD = 15 units, and $BC = 17 units. What is the area, in square units, of quadrilateral ABCD?
Answer:
The area of the quadrilateral ABCD is 114 square units
Step-by-step explanation:
We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD
First for the BAD right triangle:
AD = sqrt [BD ^ 2 - AB ^ 2]
AD = sqrt [15 ^ 2 - 12 ^ 2]
AD = sqrt [225-144]
AD = sqrt [81]
AD = 9
The area of a triangle is half the product of the base times the height, that is:
A1 = AB * AD / 2 = 12 * 9/2 = 54
Then for the second triangle in the right triangle BDC:
DC = sqrt [BC ^ 2 - BD ^ 2]
DC = sqrt [17 ^ 2 - 15 ^ 2]
DC = sqrt [289 - 225]
DC = sqrt [64] = 8
We calculate the area
A2 = DC * BD / 2 = 8 * 15/2 = 60
The total area then is:
AT = A1 + A2
AT = 54 + 60 = 114
Which means that the area of the quadrilateral ABCD is 114 square units
The rectangle shown is dilated by a scale factor of 1/5
What is the length of side A'B' and side B'D'?
Answer:
A'B'= 3 cm and B'D' = 1.6 cm
Step-by-step explanation:
First of all, we are told that the scale factor = 1/5
Now,we know that If the scale factor is less than 1, then the dilation is a reduction.
Thus, in this question the dilation is a reduction.
For us to calculate the dimensions of the dilated rectangle, we'll multiply the original dimensions by the scale factor
Thus;
A'B' = AB(1/5)
A'B' = 15(1/5) = 3 cm
B'D' = BD(1/5) = 8(1/5) = 1.6 cm
Thus, The length of each side of the dilated rectangle are;
A'B'= 3 cm and B'D' = 1.6 cm
Which phrase represents this expression?
(47−17)×4
A. 4 times the difference of 47 and 17
B. 4 times the difference of 17 and 47
C. the difference of the product of 4 times 17 and 47
D. the difference of 47 and the product of 4 times 17
Answer:
I think its A
Step-by-step explanation:
Which equation represents the hyperbola shown in the
graph?
10
8
(x - 2)2
(y + 3)
25
(-2,5) 6
(-7,3)
(1-21)
4-12-10 -8 -6 4-2
(3,3)
(x + 2)2
(y = 3) = 1
4
2 4 6
(x + 2)2
25
(y - 3)2
4
1
(232) - (7,31 = 1
(x - 2)2
25
Answer:
Step-by-step explanation:
A general equation of a hyperbola is
x^2 y^2
-------- - ------- = 1 (This applies only when the center of the hyperbola
a^2 b^2 is at (0, 0) ).
You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.
The equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
What is a hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Given that, a graph, showing hyperbola, we need to find the equation,
We have the general equation for up - down facing hyperbola as
(y - k)² / b²- (x - h)² / a² = 1.
Let's start listing the properties of this graph -
Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).
Therefore, (h, k) = (- 4,1).
This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.
Therefore, a = 3.
That gives asymptotes. Now remember that it will be in the form
y = ± b / a.
We already know a = 3, so we have to find b.
Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).
Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x.
Therefore, b = 2.
Let's substitute to equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1
Hence, the equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
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The complete question is attached
Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content
Answer:
We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
Step-by-step explanation:
We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.
The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.
Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories {means that the true average estimated calorie content in the population sampled exceeds the actual content}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories
s = sample standard deviation = 88
n = sample of individuals = 58
So, the test statistics = [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex] ~ [tex]t_5_7[/tex]
= 3.462
The value of t test statistics is 3.462.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
A project is found to have expected time T = 35.33 days and variance V = 3.22.
a. What value of z is needed to find the probability that the project will take at least 40 days? (round final answer to 2 decimals as needed)
b. What value of z is needed to find the probability that the project will take at most 40 days? (round final answer to 2 decimals as needed)
c. What value of z is needed to find the probability that the project will take at most 30 days? (round final answer to 2 decimals as needed)
Answer:
a) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
b) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
c) [tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]
Step-by-step explanation:
For this case we know that the mean for the random variable of interest is [tex]\mu = 35.33[/tex] and the variance [tex]\sigma^2 = 3.22[/tex] so then the deviation would be [tex]\sigma = \sqrt{3.22}= 1.794[/tex]
The z score is given by thsi formula:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
Part a
We want this probability:
[tex] P(X>40)[/tex]
And if we find the z score we got:
[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
And we can find this probability: [tex] P(Z>2.60)[/tex]
Part b
We want this probability:
[tex] P(X<40)[/tex]
And if we find the z score we got:
[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
And we can find this probability: [tex] P(Z<2.60)[/tex]
Part c
We want this probability:
[tex] P(X<30)[/tex]
And if we find the z score we got:
[tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]
And we can find this probability: [tex] P(Z<-2.97)[/tex]
Jakob is asked to simplify the expression –3a + 4b + 5a + (–7b).
He writes: –3a + 4b + 5a + (–7b) = –3a + 5a + 4b + (–7b).
Which property allows him to do this?
the associative property
the commutative property
the distributive property
the additive identity property
Answer: b commutative property
Step-by-step explanation: idid the test and i got it right
The property of algebra that allowed jakob simplify the given expression as stated is called; B: The commutative Property
What is a commutative Property?She wants to simplify the expression -3a + 4b + 5a + (-7b)
Now, there are different properties of algebra but the one that jakob used here is called commutative property of algebra.
Commutative property is expressed as an example like;
a + b = b + a
Thus, using commutative property, he arrived at –3a + 4b + 5a + (–7b) = –3a + 5a + 4b + (–7b).
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What is the simplest form of this expression?
(2x + 1)(x2 - 9X+11)
Answer:
2x³ - 17x² + 13x + 11
Step-by-step explanation:
(2x + 1)(x² - 9x + 11) Distribute the 2x then the 1
2x³ - 18x² + 22x + x² - 9x + 11 Combine like terms
2x³ - 17x² + 13x + 11
If this answer is correct, please make me Brainliest!
1. Solve the system of equations
-x+y=0
4x - 3y=-3
I
=
Answer:
x = -3
y = -3
Step-by-step explanation:
To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:
- x + y = 0
4x - 3y = -3
The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:
4(-x + y = 0)
-4x + 4y = 0
4x - 3y = -3
-4x and 4x cancel each other out:
4y = 0
-3y = -3
_______
y = -3
Then plug in -3 for y, into one of the equations:
- x + y = 0
- x - 3 = 0
Add 3 to both sides:
- x = 3
Divide both sides by -1:
x = -3
Jacqueline wants to make as many identical bouquets as possible using all flowers she has. What is the biggest number of such bouquets can be made out of 42 carnations, 36 tulips and 54 daffodils?
Answer:
6
Step-by-step explanation:
The greatest common factor of 36, 42, and 54 is 6:
36 = 6·6
42 = 6·7
54 = 6·9
Jacqueline's bouquets will have 6 tulips, 7 carnations, and 9 daffodils in each one. There will be 6 bouquets.
A bike tire has a diameter of 16 inches. What is the radius of the bike? What is the circumference of the bike?
Answer:
radius-8 inches cause math
circumference-50.27
Step-by-step explanation:
Rewa Delta Union RugbyCEOhas become concerned about the slow pace of the rugby gamesplayed inthe current union rugby, fearing that it will lower the spectator attendance. The CEOmeets with the union rugbymanagers and refereesanddiscusses guidelines for speeding upand makingthe gamesmore interesting and lively. Before the meeting, the mean duration of the15-sided rugbygame timewas 3 hours, 5 minutes, that is, 185 minutes.This includes all the breaks and injury times during the game. A random sample of 36 of the 15-sided rugbygames after themeeting showed a mean of 179 minutes with a standard deviation of 12 minutes.Testing at the 1% significance level, can you concludethat the mean duration of 15-sided union rugbygames has decreased after the meeting?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
which expresion has a valume of 7/12
Answer:
1/1 x 7/1 x 1/12
Is there any options?
Step-by-step explanation:
Answer:6/8 adding 1/4
Step-by-step explanation: Because im right probably
¿1 y media taza x 9?
Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]
Step-by-step explanation:
Answer: 27
-------
2
Step-by-step explanation:
Which equation represents the black line?
Which equation represents the red line?
Explain a mathematical way to find the intersection of the lines without actually graphing the lines.
Answer:
Black Line y = 3 + 2x , y = 2x +3
Red Line y = -2 - .5x. y = -.5x -2
vice versa
Step-by-step explanation:
For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x
For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.
1).
A) supplementary
B) complementary
C) comesponding
D) alternate interior
An angle whose measure is -102° is in standard position. Which quadrant does the terminal side of the angle fall?
Quadrant 1
Quadrant 2
Cuadrant 3
Cuadrant 4
Answer:3
Step-by-step explanation:
edg
Two squares are similar. The first square has sides that measure 4 inches, and the second squares has sides that measure 12 inches. The scar factor used to get from the first square to the second one is
Answer:
3
Step-by-step explanation:
Well, first off I'm assuming that by "scar factor" you mean scale factor. So if the two squares are similar then that means the sides are also similar, that means that they are equivalent. So all you have to do is 12/4 to get 3. So then to check it, you do 4 times 3 which gets you to 12.
So the final answer is 3
Determine the intercepts of the line. y=6x+13y=6x+13
Answer:
x-intercept: -13/6
y-intercept: 13
General Formulas and Concepts:
Algebra I
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityCoordinate Planes
The y-intercept is the y value when x = 0. Another way to reword that is when the graph crosses the y-axis. The x-intercept is the x value when y = 0. Another way to reword that is when the graph crosses the x-axis.Slope-Intercept Form: y = mx + b
m - slope b - y-interceptTerms/Coefficients
Step-by-step explanation:
Step 1: Define
Identify.
y = 6x + 13
Step 2: Find y-intercept
Compare given equation to slope-intercept form.
y = 6x + 13 ↔ y = mx + b
Slope m = 6
y-intercept b = 13
Step 3: Find x-intercept
Substitute y = 0.
Substitute in y [Equation]: 0 = 6x + 13[Subtraction Property of Equality] Subtract 13 on both sides: -13 = 6x[Division Property of Equality] Divide 6 on both sides: -13/6 = xRewrite: x = -13/6Connor is 4 2/3 feet tall. How many inches is that?
Answer:
hes
56 inches
hope it helps
The scatter plot for which type of data is most likely to suggest a linear association between
the two variables?
ages and heights of a group of dogs
time working out and strength of muscles
level of water in a reservoir each day and the day's date during one month
number of books returned to the library each day and the day's date over a period of one week
Plzzzz help
Answer:
level of water in a reservoir each....
Step-by-step explanation:
The scatter plot
A scatter plot is like a scatter chart or graph that uses the dots for representing the values of two different numeric variables. The horizontal value indicates the individual point data. Thus is used for observing the realtisohips between the variables.
This the answer is level of the water in a dam each day and date during 1 month.
The scatter plot can tell you the values for the set of data. The points may be given in different sizes, colors, and shapes. The data is displayed in points. The values are shown on the vertical axis. The relationship of the data can positive, negative, and neutral. The scatter plot can display a mosaic and a fluctuational diagram.Hence the option C is correct.Learn more about the which type of data.
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How many solutions does the equation -2a + 2a + 7 = 8 have
Step-by-step explanation:
-2a + 2a + 7 = 8
Solving like terms
7 = 8
= 8 - 7 = 1
Has one solution
Nora made 15 gallons of lemonade for a community picnic.
Part A
Which of the following can be used to find the number of pints of lemonade that Nora made?
15 × 2 × 2
15 × 4 × 2
15 × 3 × 2
15 × 4 × 3
Part B
How many pints of lemonade did Nora make?
Enter your answer in the box.
pints
Answer:
I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!
Answer:
B
Step-by-step explanation:
A bag of colored marbles contains 16 blue marbles, 12 red marbles, and 8 yellow marbles.
What is the theoretical probability of drawing a red marble?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
The theoretical probability of drawing a red marble is 1/3.
Step-by-step explanation:
1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.
2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.
3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.
