Answer:
k = - 11, 5
Step-by-step explanation:
By distance formula:
[tex] \sqrt{ \{ {k - ( - 3) \}}^{2} + \{5 - ( - 1) \}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + {(5 + 1)}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + {(6)}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + 36 } = 10 \\ \\ (k + 3)^{2} + 36 = {10}^{2} \\ ..(squaring \: both \: sides) \\ {k}^{2} + 6k + 9 + 36 = 100 \\ {k}^{2} + 6k + 45 - 100 = 0 \\ {k}^{2} + 6k - 55 = 0 \\ {k}^{2} + 11k - 5k - 55 = 0 \\ k(k + 11) - 5(k + 11) = 0 \\ (k + 11)(k - 5) = 0 \\ k + 11 = 0 \: or \: k - 5 = 0 \\ k = - 11 \: or \: k = 5 \\ \\ \huge \red { \boxed{k = \{ - 11, \: 5\}}}[/tex]
What is the answer to 54<45+3
Answer:
54<48
Step-by-step explanation:
If you add 45+3, you get 45.
Hope this helped.
Explain your steps to solve 3x +4/+2 = 29.
Answer:
X=18
Step-by-step explanation:
3x+4/2 = 29
Multiply both sides by 2 :
2(3x+4)/2 = 29*2
Simplify :
3x+4= 58
Subtract 4 from both sides :
3x + 4 - 4 = 58 - 4
Simplify :
3x = 54
Divide both sides by 3:
3x / 3 = 54 /3
Simplify :
X = 18
Hope it Helps :) !!!!
In one region, the September energy consumption levels for single-family homes are normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.
a. 0.1971
b. 0.3791
c. 0.2881
d. 0.0910
e. 0.8029
Answer:
a. 0.1971
Step-by-step explanation:
Z score is used to measure by how many standard deviations the raw score is above or below the mean. It is given by the formula:
[tex]z=\frac{x-\mu}{\sigma}\\ \\Where\ \mu=mean, x=raw\ score, \sigma=standard\ deviation[/tex]
Given that:
μ = 1050 kWh, σ = 218 kWh
For x = 1100 kWh
[tex]z=\frac{x-\mu}{\sigma}=\frac{1100-1050}{218} =0.23[/tex]
For x = 1225 kWh
[tex]z=\frac{x-\mu}{\sigma}=\frac{1225-1050}{218} =0.80[/tex]
From the normal distribution table, P(1100 < x < 1225) = P(0.23 < z < 0.8) = P(z < 0.8) - P(z < 0.23) = 0.7881 - 0.5910 = 0.1971
Steven Starr has an idea for a desert he is preparing to sell via food truck for restaurant week- grilled bananas with Belgian chocolate ganache. The bananas go through a 4-step process consisting of pealing, filling, grilling, and the last 2 steps are performed simultaneously- splashing and wrapping. Pealing takes 1 minute, filling takes 2 minutes and grilling takes 5 minutes. Splashing takes 3 minute and wrapping takes 3 minutes. a. The bottleneck of the process is _____, with an hourly capacity of _____.
Answer:
a) grilling
b) 12 grilling process per hour
Step-by-step explanation:
the bottleneck in this process is grilling, which slows down production by taking a considerable amount of time.
Grilling takes 5 minutes, which is the longest of any other stage of process
In one hour there are 60 minutes
The hourly rate of grilling is therefore 60/5 = 12 grilling process per hour
Find the period of the function y = 2∕3 cos(4∕7x) + 2
Answer:
7π/2
Step-by-step explanation:
The period is the value of x that makes the cosine argument be 2π:
4/7x = 2π
x = (7/4)(2π) = 7π/2 . . . the period
Ela
2
A lake covers a surface area of about 30,000 square miles.
How can you show the estimated area of the lake as a whole number multiplied by a power of ten?
Part 1 out of 4
What are you asked to find?
You need to show
as a whole number multiplied by a power of ten.
✓ Check
Next
Loop
Answer: 3 × 10⁴ miles²
Step-by-step explanation:
Given that:
Estimated Surface area of Lake = 30,000 square miles
Expressing the estimated area as a whole number multiplied by a power of ten
Hence, we are required to express the surface area in standard form:
30,000 miles ² in standard format:
30,000 is equivalent to (3 × 10,000)
3 is a whole number
10,000 = (10 * 10 * 10 * 10)= 4 th power of 10
10,000 = (10 * 10 * 10 * 10) = 10⁴
Hence,
3 × (10 * 10 * 10 * 10) = 3 × 10⁴ miles²
I need help with this
How many degrees in 2/3 of a circle
Answer:
240 degrees
Step-by-step explanation:
Felipe made sand art bottles to sell at his school's craft fair. He wanted to use 9 different colors of sand. So, he bought 1 pound of each color. Then, he filled as many 6-ounce bottles as he could. How many sand art bottles did Felipe make?
Answer: Felipe made 24 sand art bottles.
Step-by-step explanation:
Given: Total different colors of sand = 9
Weight of each color sand = 1 pound
Then, the weight of all 9 colors would be 9 × 1 = 9 pounds
Since 1 pound = 16 ounces
Then, 9 pounds = 9 × 16 = 144 ounces
capacity of each bottle = 6 ounce
Then, the number of bottles required = ( 144 ounces) ÷ 6
= 24
Hence, Felipe made 24 sand art bottles.
Answer:
24 art bottles
Step-by-step explanation:
g(x) =3x+5, h(x)=3x-4 find g(h(n))
What is the slope of the line on the graph?
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Find 2 points
(0, 2) y-int
(-4, 0) x-int
Step 2: Plug into slope formula to find slope m
[tex]m=\frac{2-0}{0-(-4)}[/tex]
[tex]m=\frac{2}{0+4}[/tex]
[tex]m=\frac{2}{4}[/tex]
[tex]m=\frac{1}{2}[/tex]
PLEASE HELP!
What percent of the circle is shaded?
Can you also explain to me please?
Answer:
75%
Step-by-step explanation:
Look at it this way since there is 8 what u could do is 1/4 so 2 of them are 25% 4 of them are 50% 6 of them are 75% and all 8 are 100%
Answer:
75%
Step-by-step explanation:
The circle is divided into 8 parts and 6 of those are shaded.
so as a fraction it would be 6/8
simplified it would be 3/4
percent is out of 100 so you have to make the denominator as 100
25 x 4 (the denominator of 3/4) is 100
25 x 3 ( the numerator of 3/4) is 75 you have to multiply both the numerator and denominator by the same number.
now you have 75/100
which is 75 percent
Hope this helps :)
Molly took part in a math quiz and scored 55 points on 30 questions. Of the questions, there were 3-point word problems, 2-point calculation questions, and 1-point multiple-choice questions. She answered 5 more 2-point questions than 1-point questions correctly. Find how many of each type of question she answered correctly.
Answer:
[tex]3\ point\ word = 5[/tex]
[tex]2\ point\ word = 15[/tex]
[tex]1\ point\ word = 10[/tex]
Step-by-step explanation:
Given
Represent
3-point word with T;
2-point with U and
1-point with V
[tex]U = 5 + V[/tex] --- (1)
If total questions is 30, then
[tex]T + U + V = 30[/tex] --- (2)
If total points is 55, then
[tex]3T + 2U + V = 55[/tex] --- (3)
Substitute 5 + V for U in (2) and (3)
[tex]T + U + V = 30[/tex] --- (2)
[tex]T + 5 + V + V = 30[/tex]
[tex]T + 5 + 2V = 30[/tex]
[tex]T + 2V = 25[/tex] ---- (4)
[tex]3T + 2U + V = 55[/tex] --- (3)
[tex]3T + 2(5 + V) + V = 55[/tex]
[tex]3T + 10 + 2V + V = 55[/tex]
[tex]3T + 10 + 3V = 55[/tex]
[tex]3T + 3V = 55 - 10[/tex]
[tex]3T + 3V = 45[/tex]
Divide through by 3
[tex]T + V = 15[/tex] ---- (5)
Subtract (5) from (4)
[tex](T + 2V = 25 )- (T + V = 15)[/tex]
[tex]T - T + 2V - V = 25 - 15[/tex]
[tex]V = 10[/tex]
Recall that:
[tex]U = 5 + V[/tex]
[tex]U = 5 + 10[/tex]
[tex]U = 15[/tex]
Substitute 10 for V in (5)
[tex]T + V = 15[/tex]
[tex]T + 10 = 15[/tex]
[tex]T = 5[/tex]
1. Write and solve an expression
for the following situation.
"9 less than the
product of 5 and 7"
Answer:
9<(5+7). the answer is 12
Step-by-step explanation:
hope it helps : )
Which statement is true regarding the graphed functions?
On a coordinate plane, a red curved line with an upward arc, labeled g of x, crosses the x-axis at (negative 2, 0), and the y-axis at (0, 4). A blue curved line with an upward arc, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).
Answer:
B
Step-by-step explanation:
I take p a p algebra
Answer:
f(0)=g(0)
Step-by-step explanation:
2020 Edg.
Survey of Ages of Participants + 5 15 25 35 45 55 65 75 85 What is the median?
The area of a square poster is 37 in.2. Find the length of one side of the poster to the nearest tenth of an inch.
Answer:
6.1 in
Step-by-step explanation:
√37=6.08276
6.1 in
The side of the square poster will be 6.1 in.
What is the area of the square?The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the square in a two-dimensional plane is called the area of the square. For the square, all the sides are equal to each other.
Given that the area of a square poster is 37 square inches the value of one side will be calculated by using the area formula:-
Area of square = Side²
Side²= √37
Side² = 6.08276
Therefore, the side of the square poster will be 6.1 in.
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Show all you work plzz
Answer:
[tex]-16+40k[/tex]
Step-by-step explanation:
[tex]8\left(-2+5k\right)[/tex]
Use the distributive law: [tex]a(b+c)=ab+ac[/tex]
[tex]8\times\left(-2\right)+8\times5k[/tex]
[tex]-16+40k[/tex]
The psychology club is having a self-proclaimed psychic come to their campus fund-raising event to demonstrate his abilities. He charges $200 for these events, and the club is charging $1.50 for tickets with a chance to have the psychic read the ticket holder’s mind. Let x represent the number of tickets sold and y represent money. Fill in the items below for the linear model.
3. Standard deviation is ________. a mean of squared differences the square root of the variance unit-free the covariance 4. Standard deviation is useful because it ________. provides a measure of deviation from the median has no units and can therefore apply to all data ignores outliers has the same units as the underlying data
Answer:
3. Standard deviation is the square root of the variance.
4. Standard deviation is useful because it has the same units as the underlying data.
Step-by-step explanation:
3. In statistics, the dispersion in a given data with respect to its mean distribution can be determined or measured by standard deviation and variance. The standard deviation of a distribution can also be determined as the square root of variance.
4. Standard deviation is measured in the same units as that of the original data. Thus it has the same units as the underlying data.
The function ()=2,708.92(1.12) − 12 models the amount of money in Caleb's investment account after years.
Caleb says this means that the initial amount in the account was $2,708.92. Is he correct? Why or why not?
A: Yes, because 2,708.92 is multiplied by the exponential term.
B: Yes, because (0)=2,708.92.
C: No, because you need to multiply 2,708.92 to find the initial amount.
D: No, because (0) is not 2,708.92.
Answer:
d i think
Step-by-step explanation:
The solution is Option D.
No , because (0) is not 2,708.92
The value of the function f ( 0 ) ≠ 2708.92
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = 2,708.92(1.12) - 12
On simplifying the equation , we get
To find the initial amount , substitute x = 0
when x = 0
Substitute the value of x in equation , we get
f ( 0 ) = 2708.92 ( 0 ) - 12
f ( 0 ) = -12
Therefore , the initial amount is -12
Hence , the value of the equation f ( 0 ) ≠ 2,708.92
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In the diagram what is the measure of angle WRS
Answer:it’s 25
Step-by-step explanation:
Why not
A 2-column table with 5 rows titled Length Conversion. Column 1 is labeled Inches, x with entries 2, 4, 7, 10, 13. Column 2 is labeled Centimeters, y with entries 5.08, 10.16, 17.78, 25.4, 33.02. What is the range of the relation of centimeters as a function of inches? {5.08, 10.16, 17.78, 25.4, 33.02} all positive integers x greater-than-or-equal-to 0 y greater-than-or-equal-to 0
Answer:
d
Step-by-step explanation:
The range of the relation of centimeters as a function of inches y ≥0.
What is Range of Function?A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range. It is only a function in a relation if each x value has exactly one y value.
Given:
Column 1 Column 2
2 5.08
4 10.16
7 17.78
10 25.4
13 33.02
As, we know the range is the output values.
So, range is {5.08, 10.16, 17.78, 25.4, 33.02}
Thus, the range is ≥ 0.
Hence, the range of the y ≥0.
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PLSSS HELP , ILL MARK BRAINLIST !!! HAVE TO GET IT RIGHT
Answer:
[tex]23[/tex]
Step-by-step explanation:
[tex]2m+n=2*m+n[/tex]
Plug in the values accordingly:
[tex]2*7+9=14+9=23[/tex]
Keshav write the multiples of 7 on his paper, but his sister accidentally erased some of them. Determine what multiple is missing. 1 , 14, 21 , 28, ____, 42
Answer:
35
Step-by-step explanation:
Endpoint: (0, 0), midpoint: (1,7)
Answer:
Step-by-step explanation:
(x + 0)/2 = 1
x + 0 = 2
x = 2
(y + 0)/2= 7
y + 0 = 14
y = 14
(2, 14)
John's extremely generous mother gave him $150 to spend on new school clothes. Shirts cost $15 each and a pair of pants cost $25. If John spent all $150 and bought 5 shirts, how many pairs of pants did he buy?
Answer: 3 pairs of pants
Step-by-step explanation:
Answer: he can still buy 3 pairs of pants
Step-by-step explanation: 15x5=75
75 + 75 = 150
he can buy 5 shirts
and 3 pairs of pants
Expression equivalent to 96+60
Answer:
60+96
156
Step-by-step explanation:
How many planes are shown in the figure?
Your answer
A jacket is on sale for $52 after a 35% discount. What is the original price?
Answer:
The final price is $33.80.You saved $18.20.
Step-by-step explanation:
Answer:
The original price was $80.
Step-by-step explanation:
The original price is x.
x is the full original price, so it is 100% of the original price.
The sale is 35%, so we subtract 35% from 100%.
100% - 35% = 65%
Since the discount was 35%, then the sale price is only 65% of the original price.
65% of the original price is $52
65% * x = 52
0.65x = 52
x = 52/0.65
x = 80
Answer: The original price was $80.
