About $290.83.
Hope this helps!
The police officer will earn approximately $290.83 more each month in his second year, as his annual salary will raise from $26,400 to $29,890.
Explanation:In this scenario, we are dealing with a salary raise and how it affects the overall monthly income. The first year, the police officer is earning $2,200 per month, which translates to an annual salary of $26,400 (since there are 12 months in a year, you can simply multiply the monthly income by 12 to find this). The second year, his annual salary will be raised to $29,890.
To see how much more they will be making a month, subtract the first year's annual salary from the second year's total ($29,890 - $26,400 = $3,490). This is the total raise for the year, but we want to find out how much more the officer will be making a month. Since the raise is distributed over 12 months, simply divide this total by 12 to get the answer. $3,490 ÷ 12 = approximately $290.83. So, the police officer will be making around $290.83 more each month in the second year.
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Simplify the following expression.
A.49
B.1/14
C.1/49
D.14
Answer:
C
Step-by-step explanation:
Using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] ⇔ [tex]\frac{1}{a^{m} }[/tex]
Hence
[tex]7^{-5/6-7/6}[/tex] = [tex]7^{-\frac{12}{6} }[/tex] = [tex]7^{-2}[/tex], then
[tex]7^{-2}[/tex] = [tex]\frac{1}{7^{2} }[/tex] = [tex]\frac{1}{49}[/tex] → C
ANSWER
C. 1/49
EXPLANATION
The given expression is
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } [/tex]
Recall that:
[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]
We apply this product rule of exponents to get:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{5}{6} + - \frac{7}{6} } [/tex]
This implies that:
[tex] {7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - \frac{12}{6} } [/tex]
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = {7}^{ - 2} [/tex]
Recall again that:
[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]
We apply this rule to get:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{ {7}^{2} } [/tex]
This simplifies to:
[tex]{7}^{ - \frac{5}{6} } \times {7}^{ - \frac{7}{6} } = \frac{1}{49} [/tex]
Need help please and thank you
Answer:
See below.
Step-by-step explanation:
This is a skewed distribution so the best measure of centre is the median.
The best measure of spread is the IQR because of the skewed distribution.
An ice cream shop makes 14 different flavors of ice cream. You can get each flavor in a waffle cone, sugar cone, cake cone, or a cup. If you are daring you can add one of these toppings rainbow sprinkles, cookie crumbs, or peanuts as a topping. How many different outcomes are possible? show work
14×3×3=126. So 126 is your answer.
Answer:
14*4*3 168
Step-by-step explanat
Which line passes through the origin?
(A) y = 3
(B) y = x − 3
(C) y = −3x
(D) y = 2x + 1
Answer:
c. y=-3x
Step-by-step explanation:
Plug in x=0 and y=0.
0=-3(0)
0=0...the origin
6. A surf board rental company charges
$25 for the first hour and $10 for each
additional hour. Which equation could be
solved to find the number, x, of
additional hours rented if the total cost of
the rental was $75?
a)25x + 10 = 75
b)25 + 10x = 75
2)75 - 25x = 10
d)25 - 10x = 75
Consider x as the missing number of hours, so 10x + 25(initial hour) and the total of the rental is $75
10x + 25 = $75
Answer
B
Solve for x: 3x - 5 = 9x + 8 - 5x
Answer:
X= -13
Step-by-step explanation:
Your first goal is to get all the X’s to one side of the equation.
So:
3x - 5 = 9x + 8 - 5x
+5x +5x
8x - 5 = 9x + 8
-9x -9x
-1x - 5 = 8
Now that you have all the X variables simplified and on one side, you make sure all of you constant terms are on the other side.
-1x - 5 = 8
+5 +5
-1x = 13
Because you can’t have a negative X, you divide the entire equation by -1.
-1x = 13
-1
x = -13
Dividing by -1 will give you the inverse of the equation which is positive one x equals negative thirteen.
Find the number of even-numbered subsets that have only even numbers from the set (1,2,3,4,5,6...100)
I would greatly appreciate a quick answer
Answer:
Step-by-step explanation:
You could use the 'brute force' method, which would be to simply write out all the possible subsets. We could avoid repetition within the subsets.
{2} would be the first subset; it contains one even number.
Next would be {2, 4}, next {2, 4, 6} ... {2, 4, 6, ... 94, 96, 98, 100}. Provided that we correctly understand what this problem is asking for, writing out and then counting all these subsets should answer the question.
15. Scott and Tara were asked to find the
area of this trapezoid:
16 cm
18 cm
24 cm
Scott wrote A = 2(24 + 16)(8).
Tara wrote A = (16 + 24)(8)
Which student is correct? Explain.
Answer:
Both Scott and Tara have responded correctly.
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
A=(1/2)[b1+b2]h
we have
b1=16 cm
b2=24 cm
h=8 cm -----> Note The height is 8 cm instead of 18 cm
substitute
A=(1/2)[16+24](8)
A=160 cm²
Verify Scott 's work
Note Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)
Remember that the Commutative Property establishes "The order of the addends does not alter its result"
so
(24+16)=(16+24)
A = (1/2)(24 + 16)(8)=160 cm²
Verify Tara's work
Note Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)
A = (1/2)(16+24)(8)=160 cm²
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
B) The sum of the interior angles in a quadrilateral is 360°.
C) Alternate interior angles formed by a transversal and parallel lines are congruent.
D) The exterior angle of a triangle is equal to the sum of the two remote interior angles.
The answer is A, Angles in an equilateral triangle are congruent.
Which fact would help you to solve for x in the diagram shown?
A) Angles in an equilateral triangle are congruent.
(PLEASE HELP) Question is worth 30 points:) The following function represents the production cost F(x) In dollars for x numbers of units produced by company 1: F(x)=0.05x^2-7x+300 The Following table represents the production cost g(x) in dollars, for x number of units produced by company 2: x: 0.6,0.8,1, 1.2, 1.4 G(x): 899.58,899.52,899.50,899.52, 899.58 based on the given information, the minimum production cost for company ____ is greater [put 1 or 2 in blank space]
Answer:
production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.05x^2 − 7x + 300
2) Table that represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
0.6 899.58
0.8 899.52
1 899.50
1.2 899.52
1.4 899.58
3) Comparison: do a table for f(x) with the same x-values of the table for g(x).
x f(x) = 0.05x^2 − 7x + 300 g(x)
0.6 295.818 899.58
0.8 294.432 899.52
1 293.05 899.50
1.2 291.672 899.52
1.4 290.298 899.58
As you can see the values of f(x) are consistently lower than the values of g(x) for the same x-values.
The minimum production cost for company 2 is around 899.50 at x = 1, while the minimum production cost of company 1 is defintely lower (lower than 292.298 for sure, in fact if you find the vertex it is 55).
Answer: Based on the given information, the minimum production cost for company 2 is greater.
Step-by-step explanation:
solve by completing the square
[tex]x ^{2} + 10x + 14 = - 7[/tex]
what is another method could you use to solve this quadratic? explain
Answer:
see explanation
Step-by-step explanation:
Given
x² + 10x + 14 = - 7 ( subtract 14 from both sides )
x² + 10x = - 21
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(5)x + 25 = - 21 + 25
(x + 5)² = 4 ( take the square root of both sides )
x + 5 = ± 2 ( subtract 5 from both sides )
x = - 5 ± 2
x = - 5 - 2 = - 7, or x = - 5 + 2 = - 3
-------------------------------------------------
The equation can also be solved by factoring
x² + 10x + 14 = - 7 ( add 7 to both sides )
x² + 10x + 21 = 0 ← in standard form
(x + 7)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x + 3 = 0 ⇒ x = - 3
The point (−3, 1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.
ANSWER
See below
EXPLANATION
The given point (-3,1) lies in the second quadrant.
In this quadrant only sine is positive.
The length of the hypotenuse formed by the right angle triangle is
[tex] {h}^{2} = {3}^{2} + {1}^{2} [/tex]
[tex] {h}^{2} = 9 + 1[/tex]
[tex]{h}^{2} = 10[/tex]
[tex]h = \sqrt{10} [/tex]
The side opposite to θ, is 1 units.
The adjacent side is 3 units.
[tex] \sin( \theta) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin( \theta) = \frac{1}{ \sqrt{10} } = \frac{ \sqrt{10} }{10} [/tex]
[tex]\cos( \theta) = - \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos( \theta) = - \frac{3}{ \sqrt{10} } = - \frac{3 \sqrt{10} }{10} [/tex]
[tex] \tan( \theta) = - \frac{opposite}{adjacent} [/tex]
[tex]\tan( \theta) = - \frac{1}{3} [/tex]
The values of sine, cosine and tangent of θ are; 1/√10, -3/√10 and -1/3 respectively.
Sine, Cosine and Tangent of anglesFrom the task content, it follows from Pythagoras theorem that;
hypothenuse = √((-3)²+1²)hypothenuse = √10On this note;
Sin θ = 1/√10Cos θ = (-3)/√10Tan θ = -1/3Read more on Trigonometric identities;
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Find the probability that the blue is even and the green is even
Answer:
1/2
Step-by-step explanation:
A die has 6 sides, in which 3 numbers (2 , 4 , 6) are even.
Simplify: 3/6 = 1/2
There is a 1/2 chance that blue is even and green is even.
~
if a rhombus has diagonals of length 20 inches and 48 inches, what is the length of its perimeter? show the work you used to find your answer.
Answer:
Perimeter of Rhombus = 104 inches
Step-by-step explanation:
To find the Perimeter of Rhombus we use the formula
Perimeter of rhombus = 4*Length
We need to find the length of rhombus.
if the rhombus has diagonals, it makes four right angled triangles (as shown in figure).
Since 4 triangles are made so, each side of triangle is half of the length of the diagonal.
In our case: Length of diagonals are: 20 and 48
but the Length of sides of triangle will be: 10 and 24
To find the side of rhombus, we can use Pythgoras theorem since the triangles are right angled.
c² = a²+b²
c² = (10)² + (24)²
c² = 100 + 576
c² = 676
√c²= √676
c = 26
So, the length of side of rhombus is 26 inches
Perimeter = 4*length
= 4*26
= 104 inches
Perimeter of Rhombus = 104 inches.
The length of the perimeter of the rhombus is 104 inches.
To find the perimeter of a rhombus with given diagonal lengths of 20 inches and 48 inches, we can use the properties of rhombuses:
Step 1. Relationship between diagonals in a rhombus:
The diagonals in a rhombus cut each other at right angles. Let the diagonal lengths be [tex]\( d_1 \)[/tex] and [tex]\( d_2 \)[/tex].
Step 2. Formula to find side length from diagonals:
The following formula can be used to find the side length ( s ) of a rhombus:
[tex]\[ s = \frac{1}{2} \sqrt{d_1^2 + d_2^2} \][/tex]
where [tex]\( d_1 = 20 \)[/tex] inches and [tex]\( d_2 = 48 \)[/tex] inches.
Step 3. Calculate the side length:
[tex]\[ s = \frac{1}{2} \sqrt{20^2 + 48^2} \][/tex]
[tex]\[ s = \frac{1}{2} \sqrt{400 + 2304} \][/tex]
[tex]\[ s = \frac{1}{2} \sqrt{2704} \][/tex]
[tex]\[ s = \frac{1}{2} \times 52 = 26 \text{ inches} \][/tex]
Step 4. Calculate the perimeter:
The perimeter ( P ) of a rhombus, with all sides equal, is determined by:
[tex]\[ P = 4 \times s = 4 \times 26 = 104 \text{ inches} \][/tex]
Therefore, the length of the perimeter of the rhombus is 104 inches.
Find the solution of this system of equations. Separate the x- and the y- values with a comma. X=6+y -8x+9y=-29
Answer:
x= 25, y = 19
Step-by-step explanation:
Solve the following system:
{x = y + 6 | (equation 1)
9 y - 8 x = -29 | (equation 2)
Express the system in standard form:
{x - y = 6 | (equation 1)
-(8 x) + 9 y = -29 | (equation 2)
Swap equation 1 with equation 2:
{-(8 x) + 9 y = -29 | (equation 1)
x - y = 6 | (equation 2)
Add 1/8 × (equation 1) to equation 2:
{-(8 x) + 9 y = -29 | (equation 1)
0 x+y/8 = 19/8 | (equation 2)
Multiply equation 2 by 8:
{-(8 x) + 9 y = -29 | (equation 1)
0 x+y = 19 | (equation 2)
Subtract 9 × (equation 2) from equation 1:
{-(8 x)+0 y = -200 | (equation 1)
0 x+y = 19 | (equation 2)
Divide equation 1 by -8:
{x+0 y = 25 | (equation 1)
0 x+y = 19 | (equation 2)
Collect results:
Answer: {x = 25 , y = 19
Answer: X= -29, Y= -267 over 10
Step-by-step explanation:
X= -29, substitute the value of X into the equation 6+y-8(-29)+9y an then solve for Y...
Hope this helps!
Which statement is true about the solution to √2x-1==1
Answer:
There are no real number solutions to this question.
The statement which is true for the equation[tex]\sqrt{2x-1} =-1[/tex] is option C which is that x=1.
What is an equation?It is a relationship between variables and it can be in the form of one variable also.
How to solve the problem?We have been given [tex]\sqrt{2x-1} =-1[/tex]
squaring both sides we get
2x-1=1
2x=1+1
2x=2
x=1
Hence the solution of the equation is x=1.
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A car travels at 48mph for 2 hours and 20 minutes how far has he travelled
Answer:
68
Step-by-step explanation:
48+2+20
The admission fee at an amusement park is $4.50 for children and $13 for adults. On a certain day, 249 people enter the park, and the admission fees collected totaled $2,013.00 how many children and how many adults were admitted?
Answer:
154 adults 94kids
Step-by-step explanation:
ASAP PLEASE HELP ME !!!!
Answer:
The correct answer is third option
The sum of any number and its opposite is 0
Step-by-step explanation:
It is given an expression,
8.29 * (-5.62 + 5.62)/5.62
To find the correct reason
Here - 5.62 + 5.62 = 0
5.62 is opposite to - 5.62
because sum of a number and its opposite is 0.
Therefore the correct answer is third option.
The sum of any number and its opposite is 0
Solve the system of equations. y = -5x + 24 y = 4x - 21 a. ( -5, -1) c. ( -1, 5) b. ( 5, -1) d. No solution
y = -5x + 24
y = 4x - 21
Since both of these equations are equal to Y, theyre equal to each other.
So we can make an equation with y = -5x + 24 in one side and y = 4x - 21 on the other.
-5x + 24 = 4x - 21
Now in order to get the value of x we need to isolate it in one side of the equation. We can do this by subtracting 24 from both sides of the equation:
-5x + 24 - 24 = 4x - 21 - 24
-5x = 4x - 45
Now we subtract 4x from both sides so the 4x shift to the other side
-5x - 4x = 4x - 4x - 45
-9x = -45
Finally divide both sides by -9 so x is by itself
(-9)÷(-9x) = -(45)÷(-9)
x = 5
Since we did all of this to BOTH sides of the equation, both sides are still equal to each other and the equation still is true.
Now apply x = 5 to either of the initial equations to find the value of Y
y = -5x + 24 or y = 4x - 21
(I'll do both but u only need one)
y = -5(5) + 24
y = -25 + 24
y = -1
y = 4(5) - 21
y = 20 - 21
y = -1
Either way, X is 5 and Y is -1
Answer (5, -1)
Final answer:
The solution to the system of equations is (5, -1), matching option b. This is found by setting both equations equal to each other, combining like terms, solving for x, and then using that value to find y.
Explanation:
To solve the system of equations, set the two equations equal to each other since they both equal y:
y = -5x + 24
y = 4x - 21
Now equate them:
-5x + 24 = 4x - 21
Add 5x to both sides:
24 = 9x - 21
Add 21 to both sides:
45 = 9x
Now divide by 9 to solve for x:
x = 5
Substitute x back into either original equation to find y:
y = -5(5) + 24
y = -25 + 24
y = -1
The solution is (5, -1), which corresponds to option b.
To check the solution, we can substitute x = 5 into both of the original equations to verify that they are true. For the first equation:
-5(5) + 24 = -25 + 24 = -1
For the second equation:
4(5) - 21 = 20 - 21 = -1
Since both substitutions lead to an identity, the solution is correct. The final answer is (5, -1), or option b.
If the length of a leg of a triangle is 39.2 and the area of the triangle is 63 what is the length of the other leg
Answer:
The length of the other leg is [tex]3.21\ units[/tex]
Step-by-step explanation:
I will assume that the triangle is a right triangle
In a right triangle the legs are perpendicular
so
The area of a right triangle is equal to
[tex]A=\frac{1}{2}(a)(b)[/tex]
where
a and b are the legs of the triangle
In this problem we have
[tex]a=39.2\ units[/tex]
[tex]A=63\ units^{2}[/tex]
substitute the values
[tex]63=\frac{1}{2}(39.2)(b)[/tex]
[tex]126=(39.2)(b)[/tex]
[tex]b=126/(39.2)=3.21\ units[/tex]
Which of the following could be folded to produce the object above?
Answer:
answer is Z
Step-by-step explanation:
Can someone plzz help me
For this case we have that by definition of trigonometric relations of a rectangular triangle that, the sine of an angle is given by the opposite leg to the angle on the hypotenuse of the triangle.
That is to say:
[tex]Sin (30) = \frac {IR} {14}[/tex]
We clear the length of the leg:
[tex]IR = 14 * sin (30)\\IR = 14 * \frac {1} {2}\\IR = 7 \ in[/tex]
Answer:
[tex]IR = 7 \ in[/tex]
en un mapa 3/16 de pulgada representa un pie. ¿ con que longitud se representan 6 1/4 pies?
I can answer your question if you could type in English plz
A refreshment stand makes 2 large servings of frozen yogurt from 3 pints. Add the line to the graph and write the equation.
Answer:
[tex]y=(2/3)x[/tex]
The graph in the attached figure
Step-by-step explanation:
Let
x-----> the number of pints
y----> the number of servings
For x=3 pints, y=2 servings
This is a proportional variation
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
so
The linear equation is equal to
[tex]y=(2/3)x[/tex]
The graph in the attached figure
Answer:
The graph is attached below
Step-by-step explanation:
A refreshment stand makes 2 large servings of frozen yogurt from 3 pints.
Equation of the line is y=mx+b
where m is the slope and b is the y intercept
2 large serving from 3 pints
So the servings over pints is 2/3
[tex]slope = \frac{2}{3}[/tex]
The y intercept is (0,0). the value of b is 0
We got m=2/3 and b=0
The equation of the line is
[tex]y=\frac{2}{3}x+0[/tex]
[tex]y=\frac{2}{3}x[/tex]
Now make a table. Assume some number for x and find out y
x y
0 0
3 2
6 4
Now make a graph using points (0,0) (3,2) and (6,4)
what is y+5=7(x-8) written in standard form
Answer:
7x-y=61
Step-by-step explanation:
The standard form is Ax+By=C.
Let's simplify the equation first.
1. Distribute: y+5=7x-56
2. Subtract 5: y=7x-61
3. Arrange into standard form: 7x-y=61
Answer
-7x+y=-61
Its the same as 7x-y=61, but in a different form
What are these Ratios in order from greatest to least? 23:24, 11:12, 7:8
Answer:
From greatest to least is 23:24 , 11:12, 7:8
Step-by-step explanation:
Hope this helps!!!
What number is 20%of 40
Answer:
20% of the number 40 is 8
20% x 40=800 divide 100 =8
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! evaluate ^3√343/512
Answer:
Step-by-step explanation:
7/8 0r 0.875
Please Help The question is in the picture
So, tangents are equal to each other when they come to a point. So, all you have to do is set 3x+10 and 7x-6 equal to each other. 3x+10=7x-6 subtract 3x from both sides 10=4x-6 and now add 6 to both sides to get 16=4x, divide by 4 on each side and x=4. If you could give me brainliest that would be super helpful!