Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
What is the first step to solve the equation 12z - 21 = 92?
12z - 21 = 92
12z - 21 + 21 = 92 + 21
12z = 113
z = 113/12
Use algebra to solve 3x+4 = 1/x
The exact solutions are x=
Х
Answer:
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{2±\sqrt{7} }{3}[/tex]
Step-by-step explanation:
3x + 4 = 1 ÷ x
3x + 4 - 4 = 1 ÷ x - 4
3x = 1 ÷ x - 4
[tex]3x=\frac{1}{x} +\frac{x(-4)}{x}[/tex]
[tex]3x=\frac{1+x(-4)}{x}[/tex]
[tex]3x=\frac{1-4x}{x}[/tex]
[tex]x(3x)=x(\frac{1-4x}{x})[/tex]
x · 3x = - 4x + 1
3x² = - 4x + 1
3x² - (- 4x + 1) = 0
3x² + 4x - 1 = 0
Ignore the A before the ±, it wouldn't let me type it correctly.
[tex]x=\frac{-b±\sqrt{b^{2}-4ac } }{2a}[/tex]
a = 3
b = 4
c = - 1
[tex]x=\frac{-4±\sqrt{4^{2}-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16-4((3)(-1)) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{16+12 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{28 } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(14) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{(2)(2)(7) } }{2(3)}[/tex]
[tex]x=\frac{-4±\sqrt{2 } \sqrt{2}\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{2(3)}[/tex]
[tex]x=\frac{-4±2\sqrt{7} }{6}[/tex]
Two separate equations
[tex]x=\frac{-4+2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2+\sqrt{7} }{3}[/tex]
[tex]x=\frac{-4-2\sqrt{7} }{6}[/tex]
[tex]x=\frac{2-\sqrt{7} }{3}[/tex]
Help please. Thank you
9514 1404 393
Answer:
(x, y) = (1, -3)
Step-by-step explanation:
The x-term has a coefficient of 1 in the first equation, making it easy to write and expression that can be substituted for x:
x = -3y -8
Using this in the second equation, we have ...
4(-3y -8) -3y = 13
-15y -32 = 13
-45 = 15y
-3 = y
Then the value of x is ...
x = -3(-3) -8 = 1
The solution is (x, y) = (1, -3).
Dannette and Alphonso work for a computer repair company. They must include the time it takes to complete each repair in their repair log book. The dot plots show the number of hours each of their last 12 repairs took. Part a. Calculate the median, mean, IQR, and standard deviation of each data set. Part b. Which measure of central tendency and spread should you use to compare the two data sets? Explain your reasoning. Part c. Determine whether there are any outliers in either data set. Dannette's Repair Times х х X X X X Х Х + 9 + 1 0 Relations 2 3 4 8 10 12 5 6 7 Repair Time (hours) Geometry Alphonso's Repair Times Groups X Trigonometry X Х X X X х X х Statistics 7 X + 3 10 9 0 4 12 Series 8 1 2 5 7 Repair Time (hours) Greek
PLZ HELP
Answer:
(a):
Dannette Alphonso
[tex]\bar x_D = 4.33[/tex] [tex]\bar x_A = 5.17[/tex]
[tex]M_D = 2.5[/tex] [tex]M_A = 5[/tex]
[tex]\sigma_D = 3.350[/tex] [tex]\sigma_A = 1.951[/tex]
[tex]IQR_D = 7[/tex] [tex]IQR_A = 1.5[/tex]
(b):
Measure of center: Median
Measure of spread: Interquartile range
(c):
There are no outliers in Dannette's dataset
There are outliers in Alphonso's dataset
Step-by-step explanation:
Given
See attachment for the appropriate data presentation
Solving (a): Mean, Median, Standard deviation and IQR of each
From the attached plots, we have:
IQR_A = 1.5 ---- Dannette
[tex]A = \{3,4,4,4,4,5,5,5,5,6,6,11\}[/tex] ---- Alphonso
n = 12 --- number of dataset
Mean
The mean is calculated
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x_D = \frac{1+1+1+1+2+2+3+7+8+8+9+9}{12}[/tex]
[tex]\bar x_D = \frac{52}{12}[/tex]
[tex]\bar x_D = 4.33[/tex] --- Dannette
[tex]\bar x_A = \frac{3+4+4+4+4+5+5+5+5+6+6+11}{12}[/tex]
[tex]\bar x_A = \frac{62}{12}[/tex]
[tex]\bar x_A = 5.17[/tex] --- Alphonso
Median
The median is calculated as:
[tex]M = \frac{n + 1}{2}th[/tex]
[tex]M = \frac{12 + 1}{2}th[/tex]
[tex]M = \frac{13}{2}th[/tex]
[tex]M = 6.5th[/tex]
This implies that the median is the mean of the 6th and the 7th item.
So, we have:
[tex]M_D = \frac{2+3}{2}[/tex]
[tex]M_D = \frac{5}{2}[/tex]
[tex]M_D = 2.5[/tex] ---- Dannette
[tex]M_A = \frac{5+5}{2}[/tex]
[tex]M_A = \frac{10}{2}[/tex]
[tex]M_A = 5[/tex] ---- Alphonso
Standard Deviation
This is calculated as:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}[/tex]
So, we have:
[tex]\sigma_D = \sqrt{\frac{(1 - 4.33)^2 +.............+(9- 4.33)^2}{12}}[/tex]
[tex]\sigma_D = \sqrt{\frac{134.6668}{12}}[/tex]
[tex]\sigma_D = 3.350[/tex] ---- Dannette
[tex]\sigma_A = \sqrt{\frac{(3-5.17)^2+............+(11-5.17)^2}{12}}[/tex]
[tex]\sigma_A = \sqrt{\frac{45.6668}{12}}[/tex]
[tex]\sigma_A = 1.951[/tex] --- Alphonso
The Interquartile Range (IQR)
This is calculated as:
[tex]IQR =Q_3 - Q_1[/tex]
Where
[tex]Q_3 \to[/tex] Upper Quartile and [tex]Q_1 \to[/tex] Lower Quartile
[tex]Q_3[/tex] is calculated as:
[tex]Q_3 = \frac{3}{4}*({n + 1})th[/tex]
[tex]Q_3 = \frac{3}{4}*(12 + 1})th[/tex]
[tex]Q_3 = \frac{3}{4}*13th[/tex]
[tex]Q_3 = 9.75th[/tex]
This means that [tex]Q_3[/tex] is the mean of the 9th and 7th item. So, we have:
[tex]Q_3 = \frac{1}{2} * (8+8) = \frac{1}{2} * 16[/tex] [tex]Q_3 = \frac{1}{2} * (5+6) = \frac{1}{2} * 11[/tex]
[tex]Q_3 = 8[/tex] ---- Dannette [tex]Q_3 = 5.5[/tex] --- Alphonso
[tex]Q_1[/tex] is calculated as:
[tex]Q_1 = \frac{1}{4}*({n + 1})th[/tex]
[tex]Q_1 = \frac{1}{4}*({12 + 1})th[/tex]
[tex]Q_1 = \frac{1}{4}*13th[/tex]
[tex]Q_1 = 3.25th[/tex]
This means that [tex]Q_1[/tex] is the mean of the 3rd and 4th item. So, we have:
[tex]Q_1 = \frac{1}{2}(1+1) = \frac{1}{2} * 2[/tex] [tex]Q_1 = \frac{1}{2}(4+4) = \frac{1}{2} * 8[/tex]
[tex]Q_1 = 1[/tex] --- Dannette [tex]Q_1 = 4[/tex] ---- Alphonso
So, the IQR is:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR_D = 8 - 1[/tex] [tex]IQR_A = 5.5 - 4[/tex]
[tex]IQR_D = 7[/tex] --- Dannette [tex]IQR_A = 1.5[/tex] --- Alphonso
Solving (b): The measures to compare
Measure of center
By observation, we can see that there are outliers is the plot of Alphonso (because 11 is far from the other dataset) while there are no outliers in Dannette plot (as all data are close).
Since, the above is the case; we simply compare the median of both because it is not affected by outliers
Measure of spread
Compare the interquartile range of both, as it is arguably the best measure of spread, because it is also not affected by outliers.
Solving (c): Check for outlier
To check for outlier, we make use of the following formulas:
[tex]Lower =Q_1 - 1.5 * IQR[/tex]
[tex]Upper =Q_3 + 1.5 * IQR[/tex]
For Dannette:
[tex]Lower = 1 - 1.5 * 7 = -9.5[/tex]
[tex]Upper = 8 + 1.5 * 7 = 18.5[/tex]
Since, the dataset are all positive, we change the lower outlier to 0.
So, the valid data range are:
[tex]Valid = 0 \to 18.5[/tex]
From the question, the range of Dannette's dataset is: 1 to 9. Hence, there are no outliers in Dannette's dataset
For Alphonso:
[tex]Lower = 4 - 1.5 * 1.5 =1.75[/tex]
[tex]Upper = 5.5 + 1.5 * 1.5 =7.75[/tex]
So, the valid data range are:
[tex]Valid = 1.75\to 7.75[/tex]
From the question, the range of Alphonso's dataset is: 3 to 11. Hence, there are outliers in Alphonso's dataset
Which is an x-intercept of the continuous function in the
table?
-2
-1
0
1
2
3
f(x)
-10
48
46
44
-2
0
(0, -6)
(3.0)
O (-6.0)
(0, 3)
Answer:
The x-intercept is the value of the variable x when the value of the function is equal to zero
so
In the table we have
(-1, 0)(−1,0) is a x-intercept, because
For x=-1x=−1 the value of the function is equal to zero
(-6, 0)(−6,0) is a x-intercept, because
For x=-6x=−6 the value of the function is equal to zero
therefore
the answer is
the continuous function in the table has two x-intercepts
(-1, 0)(−1,0)
(-6, 0)(−6,0)
i need help w this pls
Answer and Step-by-step explanation:
The answer is the second answer choice. y = 2x + 1
By looking at the graph, we see that there is a y-intercept at (0, 1), and it has a positive slope of 2.
#teamtrees #PAW (Plant and Water)
What does the digit 8 represent in 687,413?
Eight hundred thousand
Eight thousand
Eight hundred
O Eighty thousand
Answer:
Eighty thousand
Step-by-step explanation:
Look at the place value chart.
Type the correct answer in each box. Functions h and K are inverse functions, and both are defined for all real numbers Using this relationship, what is the value of each function composition?
(h o k) (3)=
(k o h)(-4b) =
Answer:
(h o k) (3) = 3
(k o h) (-4b) = -4b
Step-by-step explanation:
An inverse function is the opposite of a function. An easy way to find inverse functions is to treat the evaluator like another variable, then solve for the input variable in terms of the evaluator. One property of inverse functions is that when one finds the composition of inverse functions, the result is the input value, no matter the order in which one uses the functions in the combination. This is because all terms in a function and their inverse cancel each other and the result is the input. Thus, when one multiplies two functions that are inverse of each other, no matter the input, the output will always be the input value.
This holds true in this case, it is given that (h) and (k) are inverses. While one is not given the actual function, one knows that the composition of the functions (h) and (k) will result in the input variable. Therefore, even though different numbers are being evaluated in the composition, the output will always be the input.
A certain radioactive isotope is a by-product of some nuclear reactors. Due to an explosion, a nuclear reactor experiences a massive leak of this radioactive isotope. Fortunately, the isotope has a very short half-life of 13 days. Estimate the percentage of the original amount of the isotope released by the explosion that remains 6 days after the explosion.
Answer:
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Step-by-step explanation:
The following formula can be utilized for this question:
[tex]N = N_o (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\\frac{N}{N_o} = (\frac{1}{2})^{\frac{t}{t_{1/2}} } \\\\[/tex]
where,
[tex]\frac{N}{N_o}[/tex] = ratio of the remaining amount to the original amount = ?
t = tme passed = 6 days
[tex]t_{1/2}[/tex] = half-life = 13 days
Therefore,
[tex]\frac{N}{N_o} = (\frac{1}{2} )^{\frac{6\ days}{13\ days} }\\\\[/tex]
[tex]\frac{N}{N_o} = 0.726 = 72.6\%[/tex]
Find the volume of the frog queen building in Graz, Austria. The building is 18 meters long, 17 meters tall, and 18 meters wide
Answer: 5,508 m3
Step-by-step explanation: V= 18 x 17 x 18 = 5,508 m3
Answer:5, 508
Step-by-step explanation:
V 18×18×17=5,508
The shortest route from London to Edinburgh is 400 miles.
A lorry is expected to take 10 hours to travel this route.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 10 hours.
By how many more mph than the expected speed does the lorry travel?
Answer:
The lorry travels by 6 mph more than the expected speed.
Step-by-step explanation:
Velocity formula:
Velocity is distance divided by time, that is:
[tex]v = \frac{d}{t}[/tex]
Shortest route:
400 miles in 10 hours, which means that [tex]d = 400, v = 10[/tex]. So
[tex]v = \frac{d}{t} = \frac{400}{10} = 40[/tex]
In mph.
The lorry actually travels by a different route which increases the distance by 15%, but it still arrives in 10 hours.
Distance is multiplied by 100% + 15% = 115% = 1.15, so:
[tex]d = 1.15*400 = 460[/tex]
Then
[tex]v = \frac{d}{t} = \frac{460}{10} = 46[/tex]
46 mph
By how many more mph than the expected speed does the lorry travel?
46 - 40 = 6 mph
The lorry travels by 6 mph more than the expected speed.
Find the volume of a sphere with a diameter of 4 inches. Use 3.14 for π
.
Round your answer to the nearest hundredth.
The volume of the sphere is cubic inches.
Answer:
33.51 cubic inches
Step-by-step explanation:
Formula for volume of a sphere is V= 4 /3 · π · r3
We know the diameter is 4, and the radius is half the diameter, so the radius is 2.
V = 4 /3 · π · [tex]2^{3}[/tex]
≈ 33. 51032
Rounded to the nearest hundreth is 33.51.
What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
O A. 14 square units
O B. 6 square units
O c. 48 square units
O D. 24 square units
HELP PLEASE WITH THESE IM SO LOST AND NEED HELP! 1-4!
Answer:
1.tenisha
2.1\5+1\3=1\×
3.n-12=1\3(n+2)
4.500×=120
Which equation can be simplified to find the inverse of y = 2x2
Answer: d
Step-by-step explanation:
edge 2020
Nikki bought a patio set on sale for $480. The original price was $850. What was the rate of discount?
Round your answer to the the nearest tenth of a percent
Answer:
43.5 % decrease
Step-by-step explanation:
Take the original price and subtract the new price
850-480
370
Divide by the original price
370/850
.435294118
Change to percent form by multiplying by 100
43.5294118 % decrease
43.5 % decrease
What number must you add to complete the square? x^2+26x=11
Answer:
[tex] {x}^{2} + 26x = 11 \\ x = 0.4 \: and \: - 26.4[/tex]
5 x 10 - 2 = ??
HALP MOIIIIIIIIIIIIIIIIIIIIII
Answer:
48
Step-by-step explanation:
the answer is 48 I got this answer by multiplying 5 by 10 and subtracting is from 2 which gives me 50 - 2 which is 48
Answer:
48
Step-by-step explanation:
5×10-2=50-2
=48
hope it helps!!
What is 2 3 of 99kg?
Step-by-step explanation:
[tex] \frac{2}{3} \times \frac{99}{1} = 66 \: kg[/tex]
Determine the equation of the circle shown in the graph.
Answer:
B.
Step-by-step explanation:
The equation of a circle with center at (h, k) and radius r is
[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]
We have center at (-5, 0). That makes h = -5, and k = 0.
The radius is 3, so r = 3.
[tex] (x - (-5))^2 + (y - 0)^2 = 3^2 [/tex]
[tex] (x + 5)^2 + y^2 = 9 [/tex]
Answer: B.
Answer:
B
Step-by-step explanation:
The equation of a circle has the form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h, k) is the center of the circle and r is the radius.
From the graph, we can see that the center of the circle is at (-5, 0). So, (h, k) is (-5, 0), where h = -5 and k = 0.
And by counting, we can determine that the radius of the circle is three units. Hence, r = 3.
Substitute the information into the equation:
[tex](x-(-5))^2+(y-(0))^2=(3)^2[/tex]
Simplify. Therefore, our equation is:
[tex](x+5)^2+y^2=9[/tex]
Our answer is B.
The ratio of girls to boys in a particular classroom is 4:3. What fraction of the total number of students are boys?
The ratio of boys to the total number of students in a particular classroom is
Answer:
3:7
Step-by-step explanation:
We know that there are 4 girls and 3 boys and 4+3=7.
A company manufactures two products. Market research and available resources require the following
constraints:
• The number of units of product A manufactured, 2, is at most 500 units more than twice the number
of units of product B. y.
• The square of the company's profit is equal to the sum of 35 times the number of product A units
sold and 50 times the number of product B units sold.
If the company expects weekly profits to exceed $22,500, which pair of inequalities represents these
constraints?
will give brainliest + 50 points :)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of product A and y represent the number of product B, hence:
x ≤ 500 + 2y (1)
Also:
35x + 50y > 22500² (2)
The inequalities that represent these constraints are x ≤ 500 + 2y and 35x + 50y > 22500²
Find out more on equation at: https://brainly.com/question/2972832
#SPJ2
what is the evaluation 7w -14 for w = 9
Answer:
7w - 14
if w = 9
7(9) - 9
63 - 9
w=57
Two towers A and B are 45m and 30m high. Tower A lies to the west and B to the east of a man 1.5m tall. From the mans eye level, the angle of elevation of the top of A and B are 66° and 28° respectively. Calculate correct to three signigicant fugures the distance between A and B.
Answer:
73.0m
Step-by-step explanation:
see the attachment. Hope it helps.
Assuming p: she is beautiful,q :she is clever,the verbal form of ~p^ (~q) is she is beautiful but not clever. she is beautiful and clever she is not beautiful and not clever.she is beautiful or not clever.
Answer:
C. she is not beautiful and not clever.
Step-by-step explanation:
A. she is beautiful but not clever. B. she is beautiful and clever
C. she is not beautiful and not clever.
D. she is beautiful or not clever.
p: she is beautiful
q :she is clever
~p^ (~q) in verbal form
~p = she is not beautiful
~q = she is not clever
~p^ (~q) = she is not beautiful and not clever.
C. she is not beautiful and not clever.
Consider all four-digit numbers that can be made from the digits 0-8 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 4000
Answer:
The probability is:
P = 0.375
Step-by-step explanation:
First, we need to find the total number of four-digit numbers that can be made with the digits 0-8, such that the first digit can not be zero.
To do this, we first need to find the number of selections that we have, in this case, there are 4, one for each digit in our 4-digit number.
Now let's count the number of options that we have for each one of these selections:
first digit: we have 8 options (because the 0 can not be here)
second digit: we have 9 options (because now the zero can be taken)
third digit: we have 9 options
fourth digit: we have 9 options.
The total number of combinations is equal to the product of all the numbers of options, this is:
C = 8*9*9*9 = 5,832
Now we need to find how many of these are less or equal than 4000.
So now let's count the options again:
first digit: 3 options {1, 2, 3}
second digit: 9 options
third digit: 9 option
fourth digit: 9 options
Total number of combinations:
C' = 3*9*9*9 = 2,187
Here we should also count the combination for the number 4000 itself, as it was not counted in our previous calculation, then we have:
C' = 2,187 + 1 = 2,188 combinations.
The probability of randomly choosing a number that is smaller than or equal to 4000 will be equal to the quotient between the number of combinations that are smaller than or equal to 4000 (2,188 combinations) and the total number of combinations (5,832)
this is:
P = 2,188/5,832 = 0.375
2,45,250 students appeared for an entrance examination. If 94,750 students did not get admission, find how many students got admission.
can i please get the answer
Answer:
2.45.250- 94.750
= 92. 2975. this is the learners who got the admission
Answer:
1,50,500 students
Step-by-step explanation:
Hope this helps... vote as brainliest
If a star is 5,699,999,999,999,999 meters from earth, how long does it take light to travel from earth to the star?
Answer
19.013.153,42629466 giây
Step-by-step explanati
van toc ánh sán =299.792.458 m/s
s= v*t
t=s/v
t= 5.699.999.999.999.999/299.792.458= 19.013.153,42629466 giây
Of the animals at a pet show, 3/8 were cats and 4/8 were dogs. The rest of the animals were rabbits. What fraction of the animals were rabbits?
Answer:
1/8 Of the animals are rabbits.
Step-by-step explanation:
3/8 Cats + 4/8 Dogs = 7/8
1/8 Is all you have room left for so 1/8 would be rabbits.
Answer:
1/8.
Step-by-step explanation:
Fraction of rabbits = 1 - (3/7 + 4/8)
= 1 - 7/8
= 8/8 - 7/8
= 1/8.
help what's the answer??
