Answer:
Answer:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
Step-by-step explanation:
Standard equation of a circle: \sf (x-a)^2+(y-b)^2=r^2(x−a)2+(y−b)2=r2
(where (a, b) is the center and r is the radius of the circle)
Substitute the given center (-14, -5) into the equation:
\sf \implies (x-(-14))^2+(y-(-5))^2=r^2⟹(x−(−14))2+(y−(−5))2=r2
\sf \implies (x+14)^2+(y+5)^2=r^2⟹(x+14)2+(y+5)2=r2
Now substitute the point (-7, 5) into the equation to find r²:
\sf \implies ((-7)+14)^2+(5+5)^2=r^2⟹((−7)+14)2+(5+5)2=r2
\sf \implies (7)^2+(10)^2=r^2⟹(7)2+(10)2=r2
\sf \implies 149=r^2⟹149=r2
Final equation:
\sf (x+14)^2+(y+5)^2=149(x+14)2+(y+5)2=149
The balance in the account after 30 years will be $91,745.06, the total amount of money put into the account will be $54,000 and the total interest earned will be $37,745.06.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We can use the formula for the future value of an annuity to answer these questions:
FV = PMT(((1 + r)ⁿ - 1) / r)
a. To find how much will be in the account in 30 years, we need to calculate the future value of the annuity after 30 years of monthly deposits.
There are 12 months in a year, the number of months is:
n = 30 years × 12 months/year = 360 months
The monthly interest rate is:
r = 3% / 12 = 0.0025
Substituting the given values into the formula, we get:
FV = $150 × (((1 + 0.0025)³⁶⁰ - 1) / 0.0025)
= $91,745.06
b. To find the total amount of money put into the account, we need to multiply the monthly payment by the number of months:
Total amount = $150/month × 360 months
= $54,000
c. To find the total interest earned, we need to subtract the total amount of money put into the account from the future value of the annuity:
Total interest = $91,745.06 - $54,000
= $37,745.06
Therefore, the balance in the account after 30 years will be $91,745.06, the total amount of money put into the account will be $54,000 and the total interest earned will be $37,745.06.
To learn more on Percentage click:
https://brainly.com/question/24159063
#SPJ2
If a student does not like ballet, what is the probability that student also does not like salsa?
like salsa hate salsa total
like ballet 32 42 74
hate ballet 22 4 26
total 54 46 100
if a student does not like ballet (there is 26 that do not like ballet)..what is the probability that the student does not like salsa..of those 26 that do not like ballet, 4 do not like salsa...
4/26 = 0.1538 = 15.38% rounds to 15.4% <=
The pH of sea water is 7.6 and the PH of milk of magnesium is 10.5. 1.What are the hydrogen ion concentrations of each? 2.How many times great is the hydrogen ion concentration of the sea water than of milk of magnesium?
Answer:
2.5*10^-8 for sea water, 3.16*10^-11 for milk of magnesium, and 790 times greater
Step-by-step explanation:
We're trying to find the concentration of H+ in the solution using the pH, so
let's define pH first.
pH=-log(H+)
This equation can be re-written as
H+ = 10^(-pH), or H+ = 1/(10^pH)
The pH of sea water is 7.6, so the concentration of H+ in sea water is 10^(-7.6), which is about 2.5*10^-8
The pH of milk of magnesium is 10.5, so the concentration of H+ in milk of magnesium is 10^(-10.5), which is about 3.16*10^-11
To compare how much more the concentration of the hydrogen ion is, we just divide
(2.5*10^-8)/(3.16*10^-11) = 791, or 790 with sig figs.
which of the following are solutions
Answer:
-5 and 9
Step-by-step explanation:
To find the solutions we will factor the equation.
First we take out a 2:
[tex]2(x^2-4x-45)[/tex]
Then we can factor again:
[tex]2(x+5)(x-9)[/tex]
This provides us with the answer of:
[tex]x+5=0[/tex]
and
[tex]x-9=0[/tex]
Hence the solutions of -5 and 9.
I would like some help
Answer:
y = -2/3x + 4
Step-by-step explanation:
The y-intercept of the graph is at (0, 4) so in the equation of the line (y = mx + b), b = 4 [But all the options have that, so we have to evaluate further]The slope of the line can be calculated by where its next point on the graph isA point is (3, 2)Slope, m = 2 - 4 / 3- 0 = -2/3Equation of the line : y = -2/3x + 4
Carlos has 8 dollars and 48 cents. Alissa has 4 dollars and 14 cents. How much money does Carlos need
To give Alissa so that each of them has the same amount of money?
Answer:
.2 dollars and 17 cents
Step-by-step explanation:
Carlos has 8dollars and 48 cents --->8+0.48=8.48
Alissa has 4dollars and 14 cents--->4+0.14=4.14 let
x--->amount of money that Carlos needs to give Alissa
The linear equation that represents this situation is 8.48-x=4.14+x
solve for x2x=8.48-4.14
2x=4.34
x=2.17
therefore,the amount of money is 2 dollars and 17 cents.
thank you
by Angel osei
i need help please !!
Answer:
22x + 155
Step-by-step explanation:
9(x-3)+ 13(x+14) use distributive law
9x - 27 + 13x + `182 gather 'like' terms
(9x+13x) + ( -27+ 182) simplify
22x + 155
Find the distance between the two points in simplest radical form
(6,-4) and (1,-6)
Answer
[tex]\sqrt29[/tex]
Step-by-step explanation:
1. Write the distance formula:
[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]
2. Substitute
Substitue (6, -4) and (1, -6) into
[tex]\sqrt(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2}[/tex]
[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]
3. Calculate
[tex]\sqrt(1 - 6) ^{2} + (-6 + 4)^{2}[/tex]
[tex]\sqrt(-5) ^{2} + (-2)^{2}[/tex]
[tex]\sqrt5 ^{2} + 2^{2}[/tex]
[tex]\sqrt25 + 4[/tex]
[tex]\sqrt29[/tex]
A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between AA and BB is 55 inches.
The surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².
What is of total surface area of the rectangular prism?The total surface area of the rectangular prism is the space occupied by each of the face of it. It is the sum of area of all the faces of the prism.
Total surface area of the rectangular prism is calculated with the following formula.
[tex]A=2(lb+bh+lh)[/tex]
Here, (b) is the breath of the base (l) is the length and (h) is the height of the rectangular prism.
A rectangular prism is cut along a diagonal on each face to create two triangular prisms. The distance between A and B is 5 inches.
The length, width, and height of the prism is 5in, 3 in and 4 in long. Put these value in the above formula as,
[tex]A=2(5\times3+3\times4+5\times4)\\A=2(15+12+20)\\A=2(47)\\A=94\rm\; in^2[/tex]
The formula for surface area of one triangle prism is,
[tex]A_t=(a+b+c)l+bh[/tex]
Here, (a,b,c) are the sides of a triangle. The sides of the triangular face are 3 in, 4in and 5 in long. Thus, the surface area of it is,
[tex]A_t=(4+3 +5)5+3\times4\\A_t=(12)5+12\\A_t=72\rm\;in^2[/tex]
For the two triangular prism,
[tex]A_t=2\times72\\A_t=142\rm\; in^2[/tex]
Hence, the surface area of the rectangular prism is 94 in² and the surface area of the two triangular prisms is 142 in².
Learn more about the total surface area of a rectangular prism here;
https://brainly.com/question/15456870
#SPJ1
i will give brainliest please help
A number less than 5
⇒ x < 5
When all the numbers in the spinner are substituted in the inequality, we can see that only three numbers are less than 5.
⇒ 2, 3, and 4
Reviewing the formula to calculate probability:[tex]\dfrac{\text{Total numbers less than 5}}{\text{Total numbers in the spinner}} = \text{Probabilty of getting less than 5}[/tex]
Substituting the values in the formula:[tex]\dfrac{\text{Total numbers less than 5}}{\text{Total numbers in the spinner}} = \text{Probabilty of getting less than 5}[/tex]
[tex]\bullet \ \text{Total numbers less than five: 3}[/tex]
[tex]\bullet\ \text{Total numbers in the spinner} = 4[/tex]
[tex]\implies \boxed{\dfrac{3}{\text{4}} = \text{Probabilty of getting less than 5}}[/tex]
Final answer:Option B is correct.
A farmer sells eggs in containers holding a dozen eggs. If he has 2178 eggs, how many containers will be filled completely? How many eggs will be left over?
Answer:
~181 containers filled completely, 6 eggs left over
Step-by-step explanation:
2178 ÷ 12 (a dozen, the number of eggs per container) = 181.5 containers
181 × 12 = 2,172 eggs
2,178 eggs - 2,172 = 6 eggs left over
A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a significance level for both parts. Treatment Placebo n s Question content area bottom Part 1 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? A. : : B. : : C. : : D. : : Part 2 The test statistic, t, is enter your response here. (Round to two decimal places as needed.) Part 3 The P-value is enter your response here. (Round to three decimal places as needed.) Part 4 State the conclusion for the test. A. the null hypothesis. There sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. B. the null hypothesis. There sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. C. the null hypothesis. There sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. D. the null hypothesis. There sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean. Part 5 b. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean. 10.24 2.048 (Round to three decimal places as needed.)
There's sufficient evidence to reject the null hypothesis between the treatment group and placebo group.
How to illustrate the hypothesis?From the complete information, the value of the test statistic is -1.76 and the p-value is 0.085.
In this case, there's sufficient evidence to reject the null hypothesis. Therefore, there's evidence to warrant the rejection of the claim that the two samples are from population with same mean.
Learn more about hypothesis on:
https://brainly.com/question/15980593
Application of Geometric Series
Answer:
7.2224
Step-by-step explanation:
The value of the summation is given by the formula ...
Sn = (a1)(1 -r^n)/(1 -r) . . . . . where a1 is the first of n terms, and r is the common ratio.
Your sum has first term and ratio ...
a1 = 2(0.6) . . . . . summation term for n=1
r = 0.6
So the sum is ...
[tex]\displaystyle \sum_{n=1}^4{2(0.6^n)}=2(0.6)\dfrac{1-0.6^4}{1-0.6}=\dfrac{1.2}{0.4}(0.8704) = 2.6112[/tex]
Then the value of the entire given expression is ...
[tex]\displaystyle 2+2\sum_{n=1}^4{}2(0.6^n)=2+2(2.6112)=\boxed{7.2224}[/tex]
_____
A calculator can help you find the value.
convert [tex]\sqrt3 + i[/tex] to polar form
[tex]a~~\pm~~bi\implies r[\cos(\theta ) \pm i\sin(\theta )] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \sqrt{3}~~ + ~~i\implies \stackrel{x}{\sqrt{3}}~~ + ~~\stackrel{y}{1} i\qquad \qquad \begin{cases} r=\sqrt{x^2+y^2}\\\\ \theta =\tan^{-1}\left( \frac{y}{x} \right) \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]r=\sqrt{(\sqrt{3})^2+(1)^2}\implies r=\sqrt{3+1}\implies r=2 \\\\\\ \theta =\tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies \theta =\cfrac{\pi }{6} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 2\left[\cos\left( \frac{\pi }{6} \right)~~ + ~~i\sin\left( \frac{\pi }{6} \right) \right]~\hfill[/tex]
Check the picture below.
The Diameter of the medal is 6cm determine the radius of the medal
Answer:
3cm
Step-by-step explanation:
the radius is half the diameter
If the diameter = 6, the radius must = 3.
Hope this helps!
- profparis
solve for x
plss help
Answer:
2
Step-by-step explanation:
These two are similar triangles. 3 corresponds to 9, and x corresponds to 6. Since 3 is being multiplied by 3 to get 9, x*3 should equal 6. Therefore, x is 2.
Find the value of 2^-3
Answer:
Exact form would be 1/8
and the decimal form is 0.125
Answer:
2^-3=1/8=0.125
Step-by-step explanation:
We have a negative exponent (-3) in order to make an exponent positive write the reciprocal of the number
We get 2^-3 = 1/(2^3)
and 2^3=8
so we get 2^-3= 1/8 =0.125
NO LINKS!! Explain your answer (show the support by showing the changes in x and y on your table). If the relationship is linear, inverse or exponential, write the equation. #9
Answer:
relationship: inverseequation: y = 25/xStep-by-step explanation:
You are correct that the relationship is inverse, and that the product of x and y is a constant, 25.
__
The equation should be written so that y is a function of x:
[tex]\boxed{y=\dfrac{25}{x}}[/tex]
The x in the denominator clearly shows that y is proportional to the inverse of x.
Answer:
Linear relationship: increasing or decreasing one variable will cause a corresponding increase or decrease in the other variable.
Inverse relationship: the value of one variable decreases as the value of the other variable increases.
Exponential relationship: a constant change in the independent variable (x) gives the same proportional change in the dependent variable (y)
Question 5
As the x-value increases (by one unit), the y-value decreases.
Therefore, this is an inverse relationship.
The y-values can be calculated by dividing 25 by the x-value.
[tex]\sf y=\dfrac{25}{x}[/tex]
Classify the equation 6x + 4x - 1 = 2(5x + 4) as having one solution, infinitely many solutions, or no
solution
Enter integers or expressions to complete the solution.
6x + 4x – 1 = 2(5x + 4)
6x + 4x -1= 5x +
1 • 5x+]•4
x-1= X+8
10x - 1x - 1 = 10x -x+8
(Simplify your answers.)
Enter your answer in the edit fields and then click Check Answer.
CHEN
1
part
remaining
OP
Question
Back
Next →
Review progress
Answer:
no solution
Step-by-step explanation:
6x + 4x - 1 = 2(5x + 4) ← distribute parenthesis
10x - 1 = 10x + 8 ( add 1 to both sides )
10x = 10x + 9 ( subtract 10x from both sides )
0 = 9 ← not possible
this indicates the equation has no solution
Jason bought 3 shirts that each cost the same.He has a coupon for $10 off and he spent $65 altogether.Which equation can be used to find the cost of each shirt
Answer:
3x-10=65
Step-by-step explanation:
So, since he used the coupon, you can do 65+10=75.
The cost before the coupon is 75.
The cost of each shirt is 75/3, but that doesn't solve the question.
You can do (assume each shirt's cost is x)
3x-10=65
I could give more in depth but I can't see the options, sorry!
Answer:
(65+10) / 3= x
x would equal what each shirt costs
Step-by-step explanation:
A rectangle is graphed on a coordinate plane. The
coordinates for two of the vertices of the rectangle are
(-5, 8) and (-5, -6). What is the distance between
the two vertices?
The two vertices (-5, 8) and (-5, -6) of the rectangle have the same x-coordinates
The distance between the two vertices is 14 units
How to determine the distance between the two vertices?The vertices are given as:
(-5, 8) and (-5, -6)
The distance between the two vertices is calculated using:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
So, we have:
d = √[(-5 + 5)^2 + (8 + 6)^2]
Evaluate the sum
d = √196
Evaluate the square root
d = 14
Hence, the distance between the two vertices is 14 units
Read more about distance at:
https://brainly.com/question/7243416
Answer: 14
Step-by-step explanation:
Adía swam 7 laps in a pool Kaya swam 28 laps how many times the number of laps adía swam did kaya swim circle the letter of the correct answer
A. 4
B. 21
C. 35
D. 196
Help me my sister needs help she is in 4th grade
A circle has a diameter of
16".
What is the approximate
Circumference? What is the approximate area?
Step-by-step explanation:
to calculate circumference:
[tex]2\pi \: r[/tex]
if the diameter is 16 then the radius would be 8.
[tex]2\pi \:r \\ = 2\pi(8) \\ = 16\pi \\ =Rationalize(50.26548245744) \\circumference = 50.27[/tex]
to calculate the area of a circle:
[tex]\pi {r}^{2} \\ = \pi( {8})^{2} \\ = Rationalize(201.06192982975) \\ area = 201.06 \: ^{2} [/tex]
Group b.. pls help me
Answer:
Step-by-step explanation:
m∠ABC + m∠BAC + m∠ACB = 180°
a + 2a + 6a = 180°
9a = 180°
a = 20°
m∠ABC = 20°
m∠BAC = 2 × 20° = 40°
m∠ACB = 6 × 20° = 120°
Contort 39 to base five
i need help with this algebra question
Answer:
[tex]m=\frac{6}{7}[/tex]
Step-by-step explanation:
[tex]m=\frac{10-4}{9-2}=\frac{6}{7}[/tex]
Answer: [tex]\frac{6}{7}[/tex]
Explanation:
In the numerator we have [tex]y_2 - y_1 = 10-4 = 6[/tex] to represent the change in y, aka the rise. This is the vertical change. It's how much we go up.
The denominator has [tex]x_2 - x_1 = 9-2 = 7[/tex] to represent the run. It is the horizontal change, or how much we go to the right.
We go up 6 and to the right 7 to have a slope of [tex]m = \frac{\text{rise}}{\tex{run}} = \frac{6}{7}[/tex]
Here's how you can show the steps
[tex]m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{10-4}{9-2}\\\\m = \frac{6}{7}\\\\[/tex]
Note: To write [tex]\frac{6}{7}[/tex] on the keyboard, you can type 6/7
What whole number should replace C so that the
three values are in ascending order?
27%, С/10, 0.36
Answer:
3
Step-by-step explanation:
3/10 = .3
Find the Mean Absolute Deviation: {6, 6, 3, 4, 4}
Answer:
To find the mean absolute deviation take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set.
6,6,3,4,4 - Mean Absolute Deviation: 1.12
a triangle banner is to be made according to the specifications in the figure shown with dimensions given in inches. WOODEN STICKS WILL BE USED TO OUTLINE THE PERIMETER of the banner in order to attach the interior material. How many inches of wooden sticks will be required?
Applying the Pythagorean theorem, the amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.
What is the Pythagroean Theorem?The Pythagorean theorem is used to find a side of a right triangle, and it states that if c is the hypotenuse and a and b are the other legs, therefore: c² = a² + b².
Find the altitude/height of the triangle using the Pythagorean theorem:
height = √(13² - 5²)
height = 12
Also, use the Pythagorean theorem to find the missing side (part of the longest side of the main triangle):
missing side = √(15² - 12²) = 9
Amount of inches of wood required = Perimeter of triangle = 15 + 13 + 9 = 37 inches.
Learn more about the Pythagorean theorem on:
https://brainly.com/question/16176867
For each pair of similar figures, find the ratio of the area of the first figure to the area of the second.
answer:
[tex]\frac{4}{9}[/tex]
explanation:
the area of the larger square is 36 (6*6), and the area of the smaller square is 16 (4*4). to find the ratio of the area, simply just put 16 over 36 and simplify.
[tex]\frac{16}{36} = \frac{4}{9}[/tex]
--
if this helped, please consider giving brainliest !
A student wants to interview other students about their favorite sport. The student interviews every fifth student who enters the school in the morning. Is this a random sample or a biased sample?
A
Random sample
B
Biased sample
Answer:
Biased
Step-by-step explanation: