Leah just accepted a job at a new company where she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500. How much would Leah make as a salary after 6 years working for the company? What would be her salary after t years? Salary after 6 years: Salary after t years:
Explanation
Step 1
let s represents the salaray
let t represents the number of years she works.
she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500
hence.
[tex]S=65000+2500t[/tex]and, we have the function for the salary:
for example, after 1 year
it means, t=1
replace
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot1 \\ S=65000+2500 \\ S=67500 \end{gathered}[/tex]so After 6 years
it is, when t= 6
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot6 \\ S=65000+15000 \\ S=80000 \end{gathered}[/tex]I hope this helps you
Please help me with this problem:The data shows the number of grams of fat found in 9 different health bars.11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19What is the IQR (interquartile range) for the data? 6.25714.517.5
The interquartile range = 6.25
Explanation:The given dataset is:
11, 11.5, 10.5, 17, 14.5, 14.5, 18, 17, 19
Rearrange the data in ascending order
10.5, 11, 11.5, 14.5, 14.5, 17, 17, 18, 19
The number of terms in the data, N = 9
The lower quartile is calculated as:
[tex]\begin{gathered} Q_1=(\frac{N+1}{4})^{th}term \\ \\ Q_1=\frac{9+1}{4}^{th}term \\ \\ Q_1=2.5th\text{ term} \\ \\ Q_1=\frac{11+11.5}{2} \\ \\ Q_1=\frac{22.5}{2} \\ \\ Q_1=11.25 \end{gathered}[/tex]The upper quartile is calculated as:
[tex]\begin{gathered} Q_3=(\frac{3(N+1)}{4})^{th\text{ }}term \\ \\ Q_3=\frac{3(9+1)}{4}th\text{ terms} \\ \\ Q_3=7.5th\text{ term} \\ \\ Q_3=\frac{17+18}{2} \\ \\ Q_3=17.5 \end{gathered}[/tex]The interquartile range = Upper quartile - Lower quartile
The interquartile range = 17.5 - 11.25
The interquartile range = 6.25
5(1+s)=9s+6
----------------
Answer:
5(1+s) = -9s +6
Step-by-step explanation:
Which set of polar coordinates names the same point as (-5.5) ? ZT O O A. (5, O B. (5:59) O 5 57 4 377 O c. -5 O D. 7T 5. )
Recall that the following points represent the same point as the point (x,θ)
[tex]\begin{gathered} (-x,\theta+\pi), \\ (-x,\theta-\pi), \\ (x,\theta+2n\pi)\text{.} \end{gathered}[/tex]Now, notice that:
[tex]\frac{5\pi}{4}=\frac{4\pi}{4}+\frac{\pi}{4}=\pi+\frac{\pi}{4}\text{.}[/tex]Therefore, the point:
[tex](5,\frac{5\pi}{4})[/tex]represent the same point as the point
[tex](-5,\frac{\pi}{4})\text{.}[/tex]Answer: Option B.
what is the solution for y=2x+2 and y = 3x. I need a system of equation.
The given system of equations are,
[tex]\begin{gathered} y=2x+2 \\ y=3x \end{gathered}[/tex]Equating both equation implies,
[tex]\begin{gathered} 2x+2=3x \\ x=2 \end{gathered}[/tex]Put 2 for x in the equation y=2x+2 implies,
[tex]\begin{gathered} y=(2\times2)+2 \\ y=6 \end{gathered}[/tex]The solutions are x=2 , y=6.
Consider the equation: x2 – 3x = 18A) First, use the "completing the square" process to write this equation in the form (x + D)² =or (2 – D)? = E. Enter the values of D and E as reduced fractions or integers.=z? - 3x = 18 is equivalent to:– 3rPreview left side of egn:B) Solve your equation and enter your answers below as a list of numbers, separated with a commawhere necessary.Answer(s):
Part A.
The quadratic equation,
[tex]ax^2+bx+c=0[/tex]is equivalent to
[tex]a(x+\frac{b}{2a})^2=\frac{b^2}{4a}-c[/tex]In our case a=1, b=-3 and c=-18. Then, by substituting these value into the last result, we have
[tex](x+\frac{-3}{2(1)})^2=(\frac{-3}{2(1)})^2+18[/tex]which gives
[tex]\begin{gathered} (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9}{4}+18 \\ (x-\frac{3}{2})^2=\frac{9+72}{4} \\ (x-\frac{3}{2})^2=\frac{81}{4} \end{gathered}[/tex]Therefore, the answer for part A is:
[tex](x-\frac{3}{2})^2=\frac{81}{4}[/tex]Part B.
Now, we need to solve the last result for x. Then, by applying square root to both sides, we have
[tex]x-\frac{3}{2}=\pm\sqrt[]{\frac{81}{4}}[/tex]which gives
[tex]x-\frac{3}{2}=\pm\frac{9}{2}[/tex]then, by adding 3/2 to both sides, we obtain
[tex]x=\frac{3}{2}\pm\frac{9}{2}[/tex]Then, we have 2 solutions,
[tex]\begin{gathered} x=\frac{3}{2}+\frac{9}{2}=\frac{12}{2}=6 \\ \text{and} \\ x=\frac{3}{2}-\frac{9}{2}=\frac{-6}{2}=-3 \end{gathered}[/tex]Therefore, the answer for part B is: -3, 6
use the diagrams to answer the following questions Number 9
GIVEN:
We are given the circle with radius 5 units as shown in diagram number 9.
Required;
To determine the
(a) Diameter
(b) Circumference
(c) Area
Step-by-step solution;
The diameter of any given circle is twice the length of the radius.
This means for the circle given, we have;
[tex]\begin{gathered} Radius=5 \\ \\ Diameter=2\times R \\ \\ Diameter=2\times5 \\ \\ Diameter=10 \end{gathered}[/tex]The circumference of a circle is given by the formula;
[tex]C=2\pi r[/tex]Taking the value of pi as,
[tex]\pi=3.14[/tex]We now have the circumference as;
[tex]\begin{gathered} C=2\times3.14\times5 \\ \\ C=31.4\text{ }units \end{gathered}[/tex]The area of a circle is given by the formula;
[tex]A=\pi r^2[/tex]Therefore, we now have;
[tex]\begin{gathered} A=3.14\times5^2 \\ \\ A=3.14\times25 \\ \\ A=78.5\text{ }units^2 \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} Diameter=10\text{ }units \\ \\ Circumference=31.4\text{ }units \\ \\ Area=78.5\text{ }units^2 \end{gathered}[/tex]Which sequence is generated by the function f(n+1)(n)-2for f(1)=10?
Given the following:
[tex]\begin{gathered} f(n+1)=f(n)-2 \\ \text{where f(1)=10} \end{gathered}[/tex]To generate the sequence, we have:
[tex]\begin{gathered} \text{when n=1} \\ f(1+1)=f(1)-2 \\ f(2)=10-2=8 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=2} \\ f(2+1)=f(2)-2 \\ f(3)=8-2=6 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=3} \\ f(3+1)=f(3)-2_{} \\ f(4)=6-2=4 \end{gathered}[/tex][tex]\begin{gathered} \text{when n=4} \\ f(4+1)=f(4)-2 \\ f(5)=4-2=2 \end{gathered}[/tex]Hence, the correct option is Option D
Given that y varies directly with x, and y=28 when x=7 What is y when x=52
Answer:
y=208
Explanation:
If y varies directly with x, the equation of variation is:
[tex]y=kx[/tex]When y=28 and x=7
[tex]\begin{gathered} 28=7k \\ k=\frac{28}{7} \\ k=4 \end{gathered}[/tex]The equation connecting y and x is:
[tex]y=4x[/tex]Therefore, when x=52
[tex]\begin{gathered} y=4\times52 \\ y=208 \end{gathered}[/tex]What’s 51,053 minus 12,947?
Answer:
The answer you're looking for would be 38,106.
Step-by-step explanation:
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
I sent the attachment cuz I rather not type :3
If two matrices are equal, then each of its elements must be equal.
If:
[tex]\begin{bmatrix}{a+3} & {4} \\ {6} & {b-1}\end{bmatrix}=\begin{bmatrix}{-3} & {4} \\ {6} & {2}\end{bmatrix}[/tex]This means that:
[tex]\begin{gathered} a+3=-3 \\ 4=4 \\ 6=6 \\ b-1=2 \end{gathered}[/tex]Isolate a and b from their respective equations to find their value:
[tex]\begin{gathered} a+3=-3 \\ \Rightarrow a=-3-3 \\ \therefore a=-6 \end{gathered}[/tex][tex]\begin{gathered} b-1=2 \\ \Rightarrow b=2+1 \\ \therefore b=3 \end{gathered}[/tex]Therefore, the value of a is -6 and the value of b is 3.
An onion soup recipe calls for 3 2/3 cups of chopped onions Katrina has already chopped 1 1/3 cups of onions she wants to know how many more cups she needs to chop what X be the number of cups of onions Katrina still needs to chop write an equation to describe the situation
To determine the number of cups she still needs to chop we need to subtract the amount she already chopped to the amount she needs, then we have the equation:
[tex]x=3\frac{2}{3}-1\frac{1}{3}[/tex]This can be written as:
[tex]x+1\frac{1}{3}=3\frac{2}{3}[/tex]Now, we solve it:
[tex]\begin{gathered} x=3\frac{2}{3}-1\frac{1}{3} \\ x=\frac{11}{3}-\frac{4}{3} \\ x=\frac{7}{3} \end{gathered}[/tex]Therefore she needs to chop 7/3 more cups of onions.
Graph the solution set of each system of inequalities.19. 4x-y52x + 2y <6
The graph is given by:
Perform the indicated operations and simplify the result so there are no quotients.
Given an expression:
[tex]\csc \theta(\sin \theta+\cos \theta)[/tex]We have to simplify the given expression.
[tex]\begin{gathered} \csc \theta(\sin \theta+\cos \theta)=\csc \theta\sin \theta+\csc \theta\cos \theta \\ =\frac{1}{\sin\theta}\cdot\sin \theta+\frac{1}{\sin\theta}\cdot\cos \theta \\ =1+\frac{\cos \theta}{\sin \theta} \\ =1+\cot \theta \end{gathered}[/tex]Thus, the answer is 1 + cot theta.
If f(1) = 3, then what ordered pair is in f? (_,_)
Given:
if f(1) = 3
We are to find the ordered pair that is in f.
f(1) = 3 is a fuction.
f(1) = 3
Then,
f(x) = 3
f(x) = y
So,
f(1) = 3
Therefore,
x = 1, y = 3
So the ordered pair of f is (1, 3)
In a survey, 221people said theyhave cable TV. Thisrepresents 65% of thepeople surveyed.How many peoplewere surveyed?
1) Gathering the data
221 people = 65%
2) To find the 100% people surveyed let's set a direct proportion. And then cross multiply to have an equation:
% people
65-----------221
100-------- y
65y = 22100 Dividing both sides by 65
y =340
So, 340 people were surveyed.
Determine the equation of the line that goes through the following points. Write the final equation aslope-intercept form.(-2,6 ) and (4,-3)The equation is
The slope-intercept form is y = mx + b
Where m is the slope and b is constant represents y-intercept
given the points (-2, 6) and (4,-3)
So, the slope is = m
[tex]m=\frac{6-(-3)}{-2-4}=\frac{9}{-6}=-\frac{3}{2}=-1.5[/tex]So, y = -1.5 x + b
To find b substitute with one of the given points
So,
When x = -2 , y = 6
So,
6 = -1.5 * -2 + b
6 = 3 + b
b = 6 - 3 = 3
So, y = -1.5 x + 3
So, the equation of the line is y = -1.5 x + 3
what's the value of x for the equation 2(x-4)=6x+4
we have the equation
2(x-4)=6x+4
solve for x
Apply distributive property left side
2x-2(4)=6x+4
2x-8=6x+4
Group terms
6x-2x=-8-4
combine like terms
4x=-12
divide by 4 both sides
x=-12/4
x=-3The number line represents -4 1/2 +3 1/4 What is the sum?
Answer
Option C is correct.
-4 ½ + 3 ¼ = -1 ¼
Explanation
We are asked to solve the expression
-4 ½ + 3 ¼
To solve this, we first convert the mixed fractions into improper fractions
-4 ½ = -(9/2)
3 ¼ = (13/4)
We can then take the LCM by expressing both fractions to have the same denominatorr
-4 ½ = -(9/2) = -(18/4)
3 ¼ = (13/4)
-4 ½ + 3 ¼
= -(18/4) + (13/4)
= (-18 + 13)/4
= (-5/4)
= -1 ¼
Hope this Helps!!!
In ∆JKL, j=7.9inches, k=2 inches and l =9.8. find the measure of
By cosine rule,
[tex]\cos K=\frac{j^2+l^2-k^2}{2jl}[/tex]Where j = 7.9 inch, k = 2 inch and l = 9.8
[tex]\cos K=\frac{7.9^2+9.8^2-2^2}{2\times7.9\times9.8}=\frac{154.45}{154.84}=0.99748[/tex][tex]\begin{gathered} \cos K=0.99748 \\ K=\cos ^{-1}0.99748=4.067\approx4^o \end{gathered}[/tex]Solution: The measure of angle K is 4 degrees
Rewrite all the equation using the inverse operation.I WILL SEND PICTURES OF PROBLEM
Explanation
Step 1
[tex]\begin{gathered} a+15=32 \\ \text{subtract 15 in both sides} \\ a+15-15=32-15 \\ a=17 \end{gathered}[/tex]Step 2
[tex]\begin{gathered} b-12=75 \\ \text{add 12 in both sides} \\ b-12+12=75+12 \\ b=87 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} 9x=90 \\ we\text{ n}eed\text{ isolate x, so divide both sides by 9} \\ \frac{9x}{9}=\frac{90}{9} \\ x=10 \end{gathered}[/tex]Step 4
[tex]\begin{gathered} \frac{x}{6}=7 \\ \text{Multiply both sides by 6} \\ \frac{x}{6}\cdot6=7\cdot6 \\ x=42 \end{gathered}[/tex]I hope this helps you
Mitsu borrowed $1,250. She made 36 payments of $45.15 each. Howmuch did she pay in interest?a. $375.40b. $162.54c. $1,625.40d. $37.54
Amount borrowed = $1,250
Amount paid per payment = $45.15
Number of times payment was made = 36
This implies
The total amount paid is
[tex]36\times\text{\$}45.15=\text{\$}1625.40[/tex]Hence, the total amount paid = $1,625.40
Interest is calculated using
Interest = Total amount paid - Amount borrowed
Hence, the interest is
[tex]\begin{gathered} I=\text{\$}1625.40-\text{\$}1250 \\ I=\text{\$}375.40 \end{gathered}[/tex]Therefore, the interest she paid is $375.40
Hello, I need help simplifying question 16 i please, thanks
Given -
i. 5cot²θ + 5
To Find -
Simplification =?
Step-by-Step Explanation -
We know that
[tex]cot\theta\text{ = }\frac{\cos\theta}{\sin\theta}[/tex]So, simply putting it in the given equation:
[tex]\begin{gathered} =\text{ }5\frac{\cos^2\theta}{\sin^2\theta}\text{ + 5 } \\ \\ =\text{ 5}\frac{\lparen\cos^2\theta+\sin^2\theta\rparen}{\sin^2\theta} \\ \\ We\text{ know taht }\sin^2\theta\text{ + }\cos^2\text{ = 1} \\ \\ So,\text{ } \\ \\ =\text{ }\frac{5}{\sin^2\theta} \end{gathered}[/tex]Final Answer -
= 5/sin²θ
To find the equation of a regression line, ŷ = ax + b, you need these formulas:Sya=rstb=ỹ alA data set has an r-value of 0.553. If the standard deviation of the x-coordinates is 3.996, and the standard deviation of the y-coordinates is 6.203,what is the slope of the line to three decimal places?A. 0.858B. 1.165C. 2.807D. 0.356
Solution
- The solution steps are given below:
[tex]\begin{gathered} r=0.553 \\ S_x=3.996 \\ S_y=6.203 \\ \\ \text{ We have been given that:} \\ a=r\frac{S_y}{S_x} \\ \\ \text{ Since }a\text{ is the slope, we have that:} \\ a=0.553\times\frac{6.203}{3.996} \\ \\ a=0.8584231...\approx0.858 \end{gathered}[/tex]Final Answer
The slope is 0.858
Answer:
.0858
Step-by-step explanation:
Use gaussian elimination to solveThe buries pay their babysitter $5 per hour before 11 p.m. and $7.50 after 11p.m. One evening they went out for 5 hours and paid the sitter $35.00. What time did they come home?
Let m represents the number of hours the buries spent before 11p.m
Let n represent the number of hours the buries spent after 11p.m
m + n = 5 -----------equation (1)
5m + 7.5n = 35 -------equation (2)
Using Gaussian elimination method to solve the simultaneous equations, we have
[tex]\begin{bmatrix}{1} & {1} & {5} \\ {5} & {7.5} & {35} \\ {} & {} & \end{bmatrix}-\begin{bmatrix}{\square} & {\square} & {\square} \\ {\square} & {\square} & {\square} \\ {\square} & {\square} & {\square}\end{bmatrix}[/tex]The value of m = 1, while n = 4
This implies the buries spent 4 hours after 11 p.m
That means they come home by 3 a.m
Please help me resolve this, I’m not able Part (a)
To determine the volume of a cylinder you can use the following formula:
[tex]V=\pi r^2h,[/tex]where h is the height, and r is the radius of the cylinder.
Substituting:
[tex]\begin{gathered} r=6ft, \\ h=9ft \end{gathered}[/tex]in the formula, you get:
[tex]V=\pi(6ft)^2(9ft).[/tex]Finally, you get:
[tex]V=324\pi ft^3.[/tex]Answer: [tex]324\pi ft^3.[/tex]Pizza Orders Pizza Corner sells medium andlarge specialty pizzas. A medium Meat Lovers pizza costs$10.95, and a large Meat Lovers pizza costs $14.95. OneSaturday a total of 50 Meat Lovers pizzas were sold, andthe receipts from the Meat Lovers pizzas were $663.50.How many medium and how many large Meat Loverspizzas were sold?
Let x = number of medium Meat Lovers pizza sold
Let y = number of large Meat Lovers pizza sold
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lovers pizza sold is $663.50
This
Answer:
Let x = number of medium Meat Lovers pizzas sold
Let y = number of large Meat Lovers pizzas sold.
The cost of a medium Meat Lovers pizza is $10.95
Hence, the cost of x medium Meat Lovers pizza is $10.95x
The cost of a large Meat Lovers pizza is $14.95
Hence, the cost of y large Meat Lovers pizza is $14.95y
Since the total cost of Meat Lover's pizza sold is $663.50
This
Step-by-step explanation:
19. A wooden box has 20 cm on each edge. Find its volume.A. 875 cu. cmB. 8 000 cu. cmC. 8 875 cu. cm
Given:
Length of the edge of wooden box = 20 cm
Required:
The volume of wooden box.
Explanation:
The volume of cubical box is given as,
[tex]\begin{gathered} Volume\text{ = Edge}^3 \\ Volume\text{ = 20 cm }\times\text{ 20 cm }\times\text{ 20 cm} \\ Volume\text{ = 8000 cm}^3 \end{gathered}[/tex]Answer:
Thus the volume of the wooden box is 8000 cu. cm. The correct answer is option B.
Options for the first box are: One valid solution, two valid solutions Options for the second box are: no extraneous solutions, one extraneous solution Options for the third box: 5, 0, 2, 4
ANSWER
The equation has one valid solution and one extraneous solution.
A valid solution for x is 5
[tex]\sqrt[]{x-1}-5=x-8[/tex]
Add 5 to both-side of the equation
[tex]\sqrt[]{x-1}-5+5=x-8+5[/tex][tex]\sqrt[]{x-1}=x-3[/tex]Take the square of both-side
[tex]x-1=(x-3)^2[/tex]x - 1=x²-6x + 9
Rearrange
x² - 6x + 9 - x + 1 =0
x² - 7x + 10 = 0
We can solve the above quadratic equation using factorization method
x² - 5x - 2x + 10 = 0
x(x-5) - 2(x - 5) = 0
(x-5)(x-2)=0
Either x -5 =0 OR x-2 =0
Either x =5 or x=2
To check whether the equation is valid or non-extraneous, let's plug the values into the equation and see if it gives a true statement
For x =5
[tex]\sqrt[]{5-1}-5=5-8[/tex][tex]\sqrt[]{4}-5=-3[/tex][tex]-3=-3[/tex]The above is a true statement
For x =2
[tex]\sqrt[]{2-1}-5=2-8[/tex][tex]1-5=2-8[/tex]The above is not a true statement
Therefore, the equation has one valid solution and one extraneous solution.
A valid solution for x is 5
A square coffee table has an area of 1936 square inches. What is the length of one side of the table?
The area of square is 1936 sq.inches.
Explanation :To find the side of the coffee table.
Use the area of square .
[tex]A=side^2[/tex]Substitute the value of area to find the side.
[tex]\begin{gathered} 1936=side^2 \\ \text{side}=\sqrt[]{1936} \\ \text{side}=44in \end{gathered}[/tex]Answer :Hence the length of one side of the table is 44 in.