Answer: The family uses 3 Gb in the entire month.
Step-by-step explanation:
A month has 30 days.
If in 10 days the family uses 1Gb, then in each day the family uses:
R = 1Gb/10 days = 0.1 Gb per day.
Then in 30 days the family uses:
30days*0.1 Gb er day = 3 Gb
The family uses 3 Gb in the entire month.
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]
The area of the base of a cylinder is 45 square inches and its height is 11 inches. A cone has the same area for its base and same height. What is the volume of the cone?
Answer:
165 in³
Step-by-step explanation:
Volume of a cone is:
V = ⅓Ah
where A is the area of the base and h is the height.
V = ⅓ (45 in²) (11 in)
V = 165 in³
Choose the inequality that represents the following graph
Answer:
X ≥ 3 (D)
Step-by-step explanation:
I got it right on Khan Academy :)
find the area of the shaded region and choose the appropriate result.
Area of the larger square: (4 cm) * (4 cm) = 16 cm^2
Area of the smaller square: (2 cm) * (2 cm) = 4 cm^2
Area of the shaded region = difference between the two areas above, or 12 cm^2
Solve the inequality
Math question
Answer:
AAAAAAAAAAAAAAAAAAAA
Step-by-step explanation:
x < 7
During one year Saul takes 15 credit hours for each three quarters. Tuition and fees amount to $608 per credit hour. Textbooks average $420 per quarter. The prorated monthly cost for tuition and fees and textbooks is?
Answer:
Total textbook cost of tuition fees per month will be $ 2,356 and 25 cents
Step-by-step explanation:
To solve the exercise, we will first define the total cost per quarter.
cost of 1 credit hour = $ 601
then we solve the following:
cost of 15 credit hours = $ 601 * 15 = $ 9015
textbooks = $ 410
then we solve the following:
total cost = 9015 + 410 = $ 9425
total cost for 3 quarters = 3 * $ 9425 = $ 28275 for 12 months
we calculate as follows
Total textbook cost of tuition fees per month will be
$ 28,275 / 12 = $ 2,356 and 25 cents
Christian and Megan want to purchase a new car. The car has a base price of $16,700, options totaling $1,095, and a destination charge of $325. They read in a consumer magazine that the dealer's cost for the car is 90 percent of the base price and 87 percent of the options price. What should they estimate as the dealer's cost?
1 point
$15,764.40
$15,806.65
$16,275.15
$16,307.65
Answer:
it's B
Step-by-step explanation:
because I took the test
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
1. 10(.15)=1.5
2. 10-1.5=8.5
3. 8.5 (.15)=1.275
4. 8.5-1.275=7.225
Keep going until you get number 5 and below 1
!!!!!!!!!!!!!!!!!!!!!!!!
PLEASE MAN!
Answer:
6.14125(0.15) = 0.9211875 (below 1)
6.14125 - 0.92118 = 5.22007
Step-by-step explanation:
Given data
1. 10(.15)=1.5
2. 10-1.5=8.5
3. 8.5 (.15)=1.275
4. 8.5-1.275=7.225
continuation the sequence
5) 7.225 (0.15) = 1.08375
6) 7.225 - 1.08375 = 6.14125
7) 6.14125(0.15) = 0.9211875 (below -one)
8 ) 6.14125 - 0.9211875 = 5.2200625 (get number 5)
9) 5.2200625(0.15) = 0.783009
10) 5.2200625 - 0.783009 = 4.4370532
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
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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According to a Pew Research Center report from 2012, the average commute time to work in California is 27.5 minutes. To investigate whether the small city she lives in has a different average, a California high school student surveys 45 people she knows (her teachers, her parents, and their friends and co-workers) and finds the average commute time for this sample to be 24.33 minutes with a standard deviation of 9.53 minutes. The data are not too skewed. The null and alternative hypotheses of her study are: H0 : µ = 27.5 versus Ha : µ 6= 27.5
Required:
a. Identify the observational units for this study.
b. Identify the variable of interest and state whether it is categorical or quantitative.
c. Identify (in words and using an appropriate symbol) the parameter of interest
d. Use the 2SD approach to find a 95% confidence interval for the parameter.
e. Interpret the interval from part d. in context.
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
How does Harrison Bergeron's physical description help to create satire?
Answer:
The absurdity of Harrison's exaggerated handicaps ridicules society's obsession with equality.Step-by-step explanation:
Answer:
Step-by-step explanation:
In the year 2081, the 211th, 212th, and 213th amendments to the Constitution dictate that all Americans are fully equal and not allowed to be smarter, better-looking, or more physically able than anyone else. The Handicapper General's agents enforce the equality laws, forcing citizens to wear "handicaps": masks for those who are too beautiful, loud radios that disrupt thoughts inside the ears of intelligent people, and heavy weights for the strong or athletic.
One April, 14-year-old Harrison Bergeron, an intelligent, athletic, and good-looking teenager, is taken away from his parents, George and Hazel Bergeron, by the government. They are barely aware of the tragedy, as Hazel has "average" intelligence (a euphemism for stupidity), and George has a handicap radio installed by the government to regulate his above-average intelligence.
Hazel and George watch ballet on television.They comment on the dancers, who are weighed down to counteract their gracefulness and masked to hide their attractiveness. George's thoughts are continually interrupted by the different noises emitted by his handicap radio, which piques Hazel's curiosity and imagination regarding handicaps. Noticing his exhaustion, Hazel urges George to lie down and rest his "handicap bag", 47 pounds (21 kg) of weights locked around George's neck. She suggests taking a few of the weights out of the bag, but George resists, aware of the illegality of such an action.
On television, a news reporter struggles to read the bulletin and hands it to the ballerina wearing the most grotesque mask and heaviest weights. She begins reading in her unacceptably natural, beautiful voice, then apologizes before switching to a more unpleasant voice. Harrison's escape from prison is announced, and a full-body photograph of Harrison is shown, indicating that he is seven feet (2.1 m) tall and burdened by three hundred pounds (140 kg) of handicaps.
George recognizes his son for a moment, before having the thought eliminated by his radio. Harrison himself then storms the television studio in an attempt to overthrow the government. He calls himself the Emperor and rips off all of his handicaps, along with the handicaps of a ballerina, whom he proclaims his "Empress". He orders the musicians to play, promising them nobility if they do their best. Unhappy with their initial attempt, Harrison takes control for a short while, and the music improves. After listening and being moved by the music, Harrison and his Empress dance while flying to the ceiling, then pause in mid-air to kiss.
Diana Moon Glampers, the Handicapper General, enters the studio and kills Harrison and the Empress with a ten-gauge double-barreled shotgun. She forces the musicians to put on their handicaps, and the television goes dark. George, unaware of the televised incident, returns from the kitchen and asks Hazel why she was crying, to which she replies that something sad happened on television that she cannot remember. He comforts her and they return to their average lives.
What is the difference between the two temperatures -13°C and 10°C
Answer:
23
Step-by-step explanation:
In ΔIJK, the measure of ∠K=90°, IK = 39, JI = 89, and KJ = 80. What ratio represents the sine of ∠I?
Answer: 80/89
Step-by-step explanation:
Answer:
80/89
Step-by-step explanation:
delta math told me
The area of a rectangular wall of a barn is 171 square feet . It’s length is 10 feet longer than the width . Find the length and width of the wall of the barn
Answer:
10 x 17.1 = 171
Step-by-step explanation:
10 x 17.1 = 17.1
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]
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]
-5x+20<5 solve for x
Answer: x > 3
Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is -5x by subtracting 20 from both sides. That leaves you with -5x < -15.
To get x by itself, divide both sides by -5, but watch out.
If you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
So we have x > 3.
I have also graphed the inequality for you below.
Start with an open dot at 3. The reason for that is because x > 3 but x is not equal to 3 so we use an open dot.
Now, draw an arrow to the right to
represent all numbers greater than 3.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply.
Answer:
x = -2 or x = 1/3 thus: B & C
Step-by-step explanation:
Solve for x over the real numbers:
2 x^2 + 7 x - 2 = 2 x - x^2
Subtract 2 x - x^2 from both sides:
3 x^2 + 5 x - 2 = 0
The left hand side factors into a product with two terms:
(x + 2) (3 x - 1) = 0
Split into two equations:
x + 2 = 0 or 3 x - 1 = 0
Subtract 2 from both sides:
x = -2 or 3 x - 1 = 0
Add 1 to both sides:
x = -2 or 3 x = 1
Divide both sides by 3:
Answer: x = -2 or x = 1/3
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
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 = -13/6a bacteria population is 10,000. it triples each day. The bacteria population. p, is a function of the number of days, d.
A. p(d) = 10000(3)d
B. d(p) = 10000(3)p
C. p(d) = 3(10000)d
D. p(d) = 3(10000)p
Answer: D. p(d) = 3(10000)p
Step-by-step explanation:
The function is p(d) = 3(10000)p, where p is the bacteria population and the number of days, d. The correct answer would be option (D).
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
As per the given situation, we can write the function would be as:
⇒ p(d) = 3(10000)p
It states that the population of the bacteria, p, is equal to the starting population of 10,000 multiplied by 3 number of days, d. This function correctly represents the idea that the population triples each day.
Hence, the correct answer would be an option (D).
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can someone assist me on this
Answer:
The perimeter of the triangle would be 21.2. The area would be 18 ft^2
Step-by-step explanation:
Hope this helps :)
Attached is the work I did to get the answers
What is the circumference of the following circle?
3 cm
Answer:
the circumference is 9.42 cm
Step-by-step explanation:
3.14 · (3 cm)
c = 9.42 cm
hope this helps :-)
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.
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!
what is 7 divided by 1/3 in multiplication
Answer:21
Step-by-step explanation:
7 ➗ 1/3
when dividing fractions you have to change the divide sign to multiplication
and the denominator at the right hand side will become the numerator,the previous numerator at the right hand side will become denominator
7 x 3/1=21
1).
A) supplementary
B) complementary
C) comesponding
D) alternate interior
