Answer:
The distance between the two points is [tex]\sqrt{65} \ \text{units}.[/tex]
Step-by-step explanation:
In order to find the distance between two coordinate pairs, we can use the distance formula:
[tex]\displaystyle \bullet \ \ \ d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Our coordinate pairs need to be labeled accordingly, so we can use this naming system:
[tex]\bullet \ \ \ (x_1, y_1), (x_2, y_2)[/tex]
This assigns a name to our points:
[tex]x_1 = -5[/tex][tex]y_1 = 1[/tex][tex]x_2 = 3[/tex][tex]y_2 = 0[/tex]Therefore, we can plug these into the formula and solve:
[tex]d=\sqrt{(3-(-5))^2+(0-1)^2}\\\\d=\sqrt{(8)^2+(-1)^2}\\\\d=\sqrt{8^2+1^2}\\\\d=\sqrt{64+1}\\\\d=\sqrt{65}[/tex]
Therefore, the distance between the two points is [tex]\sqrt{65} \ \text{units}[/tex].
Bob bought the 24 fish for $51.36. How much did each fish cost him? Show your calculation.
Answer:
2.14
Step-by-step explanation:
2.14x24=51.36
The radius of a sphere is increasing at a constant rate of 7 feet per second. At the instant when the volume of the sphere is 274 cubic feet, what is the rate of change of the volume? The volume of a sphere can be found with the equation V=4/3π(r)^3. Round your answer to three decimal places.
a bag contains 3 red balls and 1 blue ball. what is the expected number of red balls in the first bag
Answer:
[tex]Expected\ Value = 3[/tex]
Step-by-step explanation:
Given
[tex]Red\ Balls = 3[/tex]
[tex]Blue\ Balls = 1[/tex]
Required
Determine the expected number of red balls
First, we calculate the probability of a red ball
[tex]P(Red\ Ball) = \frac{Red\ Ball}{Total}[/tex]
[tex]P(Red\ Ball) = \frac{3}{3 + 1}[/tex]
[tex]P(Red\ Ball) = \frac{3}{4}[/tex]
[tex]P(Red\ Ball) = 0.75[/tex]
The expected value is then calculated as:
[tex]Expected\ Value = P(Red\ Ball) * Total[/tex]
[tex]Expected\ Value = 0.75 * 4[/tex]
[tex]Expected\ Value = 3[/tex]
Find 4cos2a, if
[tex] \cos(a) = \frac{ \sqrt{3} }{2} [/tex]
If you mean to find 4 cos(2a), then recall the double angle identity for cosine:
cos(2x) = 2 cos²(x) - 1
so that
4 cos(2a) = 4 (2 cos²(x) - 1) = 4 (√3 - 1)
Can someone help with this please?
Answer:
a) Function 1 has the greatest y-intercept
b) Only function 2 has a slope less than -2
c) Function 4 has the least steep slope
Answer:
1. Function 1
2. Function 2
3. Function 4
Step-by-step explanation:
y-intercept: Function 1: 4, Function 2: 1, Function 3: -5, Function 4: -2
- Function 1 has the highest y-intercept
slope less than -2: Function 1: 2, Function 2: -4, Function 3: 5, Function 4: -1
- Function 2 has a slope lower than -2
least steep graph: Function 1: steepness 2, Function 2: steepness 4, Function 3: steepness 5, Function 4: steepness 1
- Function 4 has the steepest graph
Assume that last year in a particular state with 700000 children there were 1205 children out of 32600 in a random sample who were diagnosed with Autism Spectrum Disorder. Nationally, 1 out of 88 children are diagnosed with ASD. Is there sufficient data to show that the incident rate of ASD is higher in that state than nationally
Answer:
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
Step-by-step explanation:
The population follows a binomial distribution, and the fact that
p₀ = 1205/32600 = 0,03696 and then q₀ = 1-0,03696 = 0,9630
And both
p₀*n = 0,03696*32600 = 1205 > 10
q₀*n = 31395 > 10
The binomial distribution can be approximate to a Normal Distribution, then we need to develop a one tail test ( to the right) to evaluate if the claim " There is sufficient data to show that the incident rate is higher in the mentioned state than the national one.
Therefore:
Hypothesis Test H₀ ⇒ p₀ = p
Alternative Hypothesis Hₐ ⇒ p₀ > p
p is the population proportion mean
p = 1/88 = 0,011
We must test having a very wide Confidence Interval since the matter we are trying is public health then we choose CI = 95 %
CI = 95 % α = 5 % α = 0,05
Critical value for 0,05 is from z-table z(c) = 1,64
We compute z(s)
z(s) =( p₀ - p )/ √ p₀*q₀/n
z(s) = 0,03696 - 0,011 / √ (0,03696*0,9630)/ 32600
z(s) = 0,02596* 180,55/ √ 0,0356
z(s) = 4,687 / 0,189
z(s) = 24,9
Comparing z(s) and z(c) 24,9 > 1, 64
z(s) is out of the acceptance region and we have to reject H₀
We accept Hₐ there is enough evidence to claim that the incidence of ASD is bigger in this state than it is nationally
Solve for x. Enter the solutions from least to greatest.
(x + 7)^2 - 49 = 0
Answer:
x = -14, 0
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Completing the SquareMultiple Roots/SolutionsStep-by-step explanation:
Step 1: Define
(x + 7)² - 49 = 0
Step 2: Solve for x
Add 49 to both sides: (x + 7)² = 49Square root both sides: x + 7 = ±7Subtract 7 on both sides: x = -7 ± 7Evaluate: x = -14, 0Step 3: Check
Plug in x values into original equation to verify they are a solution.
x = -14
Substitute in x: (-14 + 7)² - 49 = 0Add: (-7)² - 49 = 0Exponents: 49 - 49 = 0Subtract: 0 = 0Here we see that 0 does indeed equal 0.
∴ x = -14 is a solution of the equation
x = 0
Substitute in x: (0 + 7)² - 49 = 0Add: 7² - 49 = 0Exponents: 49 - 49 = 0Subtract: 0 = 0Here we see that 0 does indeed equal 0.
∴ x = 0 is also a solution of the equation.
Answer:
Lesser x=-14 Greater x=0
Step-by-step explanation:
x+7)
2
−49
(x+7)
2
(x+7)
2
=0
=49
=
49
Hint #22 / 3
\begin{aligned} x+7&=\pm7 \\\\ x&=\pm7-7 \\ \phantom{(x + 7)^2 - 49}& \\ x=-14&\text{ or }x=0 \end{aligned}
x+7
x
(x+7)
2
−49
x=−14
=±7
=±7−7
or x=0
eye blue like the Atlantic and im going down like the Titanic
Answer:
how is this a question
Step-by-step explanation:
Input
х
Output
Y
1
0
1
A
5
B
31
с
46
D
25
76
Answer: 46
Step-by-step explanation:
Yes !!
use the distributive property to find the answer to 21 x 4
Answer:
21(4)
Step-by-step explanation:
=84 that's all u have to do
slope = 2; y-intercept = -1
Answer:
line equation: y= 2x-1
Slope intercept formula
y=mx+b
m is also the slope
b is the y-intercept
y=2x+(-1)
+ positive sign and -negative sign= - negative sign
y=2x-1
Answer :
y=2x-1
Help me fast pleaseeeee
Answer:
y=-2x-2
Step-by-step explanation:
Find slope and y intercept
3. Sam and Tim each have savings accounts. Every month they each put in some of their
earnings from mowing lawns. Use the tables to find the y-value of the solution to the
system shown.
х
1
2
3
4
f(x)
80
110
140
170
х
1
2
3
4
g(x)
100
120
140
160
Answer:
[tex]y = 30x +50[/tex] --- Sam
[tex]y = 20x +80[/tex] --- Tim
Step-by-step explanation:
Given
Sam Tim
х --- f(x) --------------- g(x)
1 --- 80 --------------- 100
2 --- 110 --------------- 120
3 --- 140 --------------- 140
4 --- 170 -------------- 160
Required
Determine the y value
y value implies the equation of the table
Calculating the equation of Sam
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (1,80)[/tex]
[tex](x_2,y_2) = (4,170)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{170 - 80}{4 - 1}[/tex]
[tex]m = \frac{90}{3}[/tex]
[tex]m = 30[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 80 = 30(x - 1)[/tex]
[tex]y - 80 = 30x - 30[/tex]
Make y the subject
[tex]y = 30x - 30 + 80[/tex]
[tex]y = 30x +50[/tex]
Calculating the equation of Tim
First, we need to take any corresponding values of x and y
[tex](x_1,y_1) = (1,100)[/tex]
[tex](x_2,y_2) = (4,160)[/tex]
Next, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{160 - 100}{4 - 1}[/tex]
[tex]m = \frac{60}{3}[/tex]
[tex]m = 20[/tex]
Next, we calculate the line equation using:
[tex]y - y_1=m(x-x_1)[/tex]
[tex]y - 100 = 20(x - 1)[/tex]
[tex]y - 100 = 20x - 20[/tex]
Make y the subject
[tex]y = 20x - 20+100[/tex]
[tex]y = 20x +80[/tex]
Simplify the following polynomial expression (8x^2-7x+2)+(3x^2-9x-6) help fasttt!!!!!!!!!!!!!
Answer:
11x^2 - 16x +4
Step-by-step explanation:
In order to simplify, add like terms
(8x^2-7x+2)+(3x^2-9x-6)
8x^2 + 3x^2 = 11x^2
-7x + -9x = -16x
-6 + 2 = 4
now the equation is 11x^2 - 16x +4
Ryan has a checking account balance of -$25. Write an absolute value statement to show how much money Ryan owes the bank.
Don’t understand pls help
Answer:
-1.5x + 3
Step-by-step explanation:
The Y-intercept is visible, wherever the line is touching the Y-Axes is the intercept. Use this formula to solve for slope:
Determine the equation of the line given by the graph.
A)y = -2/7x+2/5
B)y = -2/7x+5/2
C)y = -7/2x+2/5
D)y = -7/2x+5/2
Answer:
y=mx+c y= -2/7+5/2 if this is right can i get brainliest and if u need explanation just ask
Answer:
D. y = -7/2x+5/2
Step-by-step explanation:
The formula for the graph would be: y = mx + c where m is the slope and c is the y-intercept.
Based on the graph, you can see that the y-intercept is 5/2 (somewhere between 5 and 0) so A and C are out. Remaining are options B and C.
Now, the slope is either -2/7 or -7/2. We will have to calculate the slope then. I will be using the points (-1, 6) and (1, -1)
[tex]\frac{rise}{run}[/tex] = [tex]\frac{-1-6}{1-(-1)}[/tex]
= [tex]\frac{-7}{2}[/tex]
= -[tex]\frac{7}{2}[/tex] (Same as option D)
Thus, the equation would have been: -[tex]\frac{7}{2}[/tex]x + [tex]\frac{5}{2}[/tex]
Express each ratio as a unit rate. Round to the nearest tenth, if necessary.
100 miles in 2.5 hours
40 miles per hour
100
a. Yo
c.
25 miles per hour
1000
b. 250 miles per hour
d.
25
miles per hour
Please select the best answer from the choices provided
А
B
ОС
D
Answer:
c
Step-by-step explanation:
Answer:
A. 100 miles divide 2.5 hours = 40 miles per hour
Find the sum. Write your answer as a decimal.
-5.74 + 5.5 =
Answer:
-0.24
Step-by-step explanation:
Math is math i just know it in my head i do nt know how tpo explain itIn triangle ABC, angle BAC = 90
Work out the size of angle DAC AND DCA?
Quick plz:)
Answer:
Easy man it 9999
Step-by-step explanation:
Please help on number 5 and ill give brainly
Is each expression equivalent to 6 * 53? Justify your reasoning.
a. 6 * 50 + 6* 3
b. 10 * 53 -4 53
c. 6 50 + 3
d. 6 * (50 + 3)
Answer:
a, b, d. Yes c. NoStep-by-step explanation:
a. 6 * 50 + 6* 3 = 6* ( 50 + 3) = 6* 53
Yesb. 10 * 53 -4*53 = (10 - 4)*53 = 6*53
Yesc. 6 * 50 + 3 = 303
Nod. 6 * (50 + 3) = 6*53
YesAnswer:
A, B, D = Yes
C = No
6 * 50 + 6* 3 = 6* ( 50 + 3) = 6* 53
10 * 53 -4*53 = (10 - 4)*53 = 6*53
6 * 50 + 3 = 303
6 * (50 + 3) = 6*53
(a) 12 is 15% of what?
Please help
multiple choice
picture included
will appreciate it if you help!
Answer:
D
Step-by-step explanation:
The quotient of 2 and n is 2/n, not n/2, and if it's at most 6 that means it can equal 6 but can't go above it, so it's less than or equal to six. Hope this helped!
please give answer please!!!!!!!!!!!!
All of them produce an angle of 90 degrees, therefore
90 degrees x 4 = 360 degrees
150 pounds to 135 pounds
Answer:
15 pounds
Step-by-step explanation:
150-135
Answer:
15 pounds
Step-by-step explanation:
In a certain Algebra 2 class of 24 students, 9 of them play basketball and 13 of them
play baseball. There are 2 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
The probability that a student who is chosen randomly from the class who plays basketball or baseball is 11/24.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that In a certain algebra 2 class of 24 students, 9 of them play basketball and 13 of them play baseball. There are 2 students who play both sports.
2+5+4 =11
Expect the 13 people/students who didn't play,
Total people 24
P = 24-13=11
P = 11/24
The probability will be equal to 11/24.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ1
Carmen has taken out a loan for $800 to buy a car. She plans to pay back the loan at a rate of $40 per month. Ramona has borrowed $500 to buy a car, which she plans to pay back at a rate of $20 per month.
How long will it take Ramona to pay back her loan?
Answer:
It will take Ramona 25 months or 2 years and 1 month to pay back for the car.
The manager of a grocery store has selected a random sample of 100 customers. The average length of time it took these 100 customers to check out was 3.0 minutes. It is known that the standard deviation of the checkout time is 1 minute. Refer to Exhibit 8-2. If the confidence coefficient is reduced to .80, the standard error of the mean _____.
Answer:
The standard error of the mean remains unchanged.
Step-by-step explanation:
Given that:
The standard error (S.E) of the mean [tex]= \dfrac{\sigma}{\sqrt{n}}[/tex] with is independent of confidence coefficient.
The margin of error [tex]E = z \times S.E[/tex]
This explains the claim that as the confidence coefficient reduces, the z-value also reduces, so as the Margin of error (E) but the standard error will always remain unchanged.
i.e.
From the question;
sample size n = 100
standard deviation = 1
mean = 3.0
The standard error (S.E) of the mean [tex]= \dfrac{1}{\sqrt{100}}[/tex]
= 0.1
So, if the confidence coefficient is reduced to 0.80, the standard error of the mean remains unchanged.
Please help me ASAP
How many pavers are needed to cover the patio?
Answer:
270
Step-by-step explanation:
✔️Area of the Patio = bh
b = 12 ft = 144 in.
h = 10 ft = 120 in.
Area of Patio = 144*120 = 17,280 in.²
✔️Area of Brick Paver = bh
b = 8 in
h = 8 in
Area of the Brick Paver = 8*8 = 64 in.²
The number of quaver needed to cover the Patio = area of Patio ÷ area of one brick quaver
= 17,280/64 = 270