Answer:
$10,050
Step-by-step explanation:
To find a percent of a number, multiply the percent by the number. First, change the percent to a decimal by dividing it by 100.
15% of $67,000 =
= 15% * $67,000
= 0.15 * $67,000
= $10,050
The table below shows selected points from a function.
Fist section box answer choice: Constant, not Constant
second section box answer choice: linear, non-linear
The rate change of interval for the given table is Constant , so the function a linear function.
Step-by-step explanation:
A linear function is defined as a function which yields a line in a graph and the rate of change(constant) is called as slope.
Since the rate is constant, then function will result in a straight line.
From the given table the slope m=1 and it changes constantly.
The linear equation formula is y=mx+c.
where m is the slope and c is the y-intercept.
The linear equation for the given table is y=x+1.
∴ The rate change of interval for the given table is Constant , so the function a linear function.
If the graph for a function has any shapes other than a straight line then it doesn't have a constant slope and it will be a non-linear function.
What part of an hour elapses from 4:56 P.M. to 5:32 P.M.?
Answer:
[tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]
Step-by-step explanation:
Given hours is from 4:56 P.M. to 5:32 P.M.
Now, finding the part of an hour elapases.
We know the starting time is 4 minutes to 5:00 P.M and end time is 32 minutes past 5 P.M.
∴ Total times elapses= [tex]4\ minutes + 32\ minutes= 36\ minutes[/tex]
Hence, 36 minutes elapses out of an hour.
Remember; 1 hours= 60 minutes
Next, finding the fraction of an hour elapses.
[tex]Part\ of\ an\ hour\ elapses= \frac{36}{60}[/tex]
∴ [tex]Part\ of\ an\ hour\ elapses= \frac{3}{5} \ hour[/tex]
Hence, [tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex] from 4:56 P.M. to 5:32 P.M.
explain how you know the numbers of the decimal places that should be in the product when you multiply two decimal numbers together
Answer:
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
Step-by-step explanation:
Let's remember that multiplying decimals is the same as multiplying whole numbers except that you have to put the decimal point in the answer. When you multiply decimals, the decimal point is placed on the product so that the number of decimal places in the product is the sum of the decimal positions of the factors.
Example:
214 * 32 = 6,848
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
7 * 11 = 77
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
You have just bought a new Sony 55” 3D television set for $2300. The TV’s value decreases at a rate of $250 per year. Construct a linear function to represent this situation. Clearly indicate what your variables represent.
Answer:
2300-x(250) is the best i could think of hope it helps
Step-by-step explanation:
We need to represent the value of a TV whose value decreases yearly.
The required equation is [tex]y=2300-250x[/tex]
The cost of the TV set is $2300.
The decrease in value is $250 per year.
Let [tex]x[/tex] be the number of years that has passed after buying the TV
and [tex]y[/tex] be the cost of TV after [tex]x[/tex] years have passed.
The linear equation that represents the situation is [tex]y=2300-250x[/tex]
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Solving a right triangle ‼️ Can someone help me find A,a and c❓ (Round to the nearest tenth)
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for A
A = 180° - (90 + 48)° = 180° - 138° = 42°
----------------------------------------------------------
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{a}[/tex]
Multiply both sides by a
a × tan48° = 18 ( divide both sides by tan48° )
a = [tex]\frac{18}{tan48}[/tex] ≈ 16.2 ( to the nearest tenth )
-----------------------------------------------------------
sin48° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{c}[/tex]
Multiply both sides by c
c × sin48° = 18 ( divide both sides by sin48° )
c = [tex]\frac{18}{sin48}[/tex] ≈ 24.2 ( to the nearest tenth )
Given Angle 1 = Angle 2,
find x.
Answer:
x = 6
Step-by-step explanation:
Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is
[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross- multiply )
x(x - 4) = 12 ← distribute left side
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
However, x > 0 , thus x = 6
“ The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $15 per ticket to the planetarium. The second day they paid $90 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club. An expression that represents the total cost in dollars for two days for the n members of the club is given by .”
Answer:
[tex]x = \$187n[/tex]
Step-by-step explanation:
let x be the total cost in dollars for two days for the n members
Given:
The first day the members paid $70 for transportation plus $15 per ticket to the planetarium.
The second day they paid $90 for transportation plus $12 per ticket to the geology museum.
We need to write an an expression to represent the total cost in dollars for two days for the n members of the club.
Solution:
First day each member pay $70 for transportation and $15 for ticket,
[tex]Cost\ per\ member\ for\ the\ first\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = 70+15[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = \$85[/tex]
Therefore, cost for n members for the first day.
[tex]Cost\ for\ n\ member\ for\ the\ first\ day = \$85n[/tex]
Similarly for the second day each member pay $90 for transportation and $12 for ticket,
[tex]Cost\ per\ member\ for\ the\ second\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = 90+12[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = \$102[/tex]
Therefore, .
[tex]Cost\ for\ n\ member\ for\ the\ second\ day = \$102n[/tex]
Now, we write an expression to represent the total cost in dollars for two days for the n members of the club, so cost for n members for two days is equal to sum of the two days expenses for n members.
[tex]Cost\ for\ n\ member\ for\ the\ two\ day = \$85 + \$102n[/tex]
[tex]x = \$85n + \$102n[/tex]
[tex]x = \$187n[/tex]
Therefore, total cost for two days for the n members [tex]x = \$187n[/tex]
Which of these equivalent
ratios is the unit rate?
90 miles
3 hours
60 miles
2 hours
30 miles
1 hour
Answer:
30 miles/1 hour is the unit rate.
Step-by-step explanation:
This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (5,4) and (2,-7)?
Answer:
slope = [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, - 7)
m = [tex]\frac{-7-4}{2-5}[/tex] = [tex]\frac{-11}{-3}[/tex] = [tex]\frac{11}{3}[/tex]
What is the x intercept and y intercept of this equation.
Answer:
x intercept is 15 and y intercept is -3.75
Step-by-step explanation:
The first thing is to form equation with the given tow point using the formula
y-y1/x - x1 = y2 - y1/ x2 - x1
y + 5/x + 5 = -2 + 5/7 + 5
y + 5/x + 5 = 3/ 12
3x + 15 = 12y + 60
12y - 3x = -45
On x intercept y = 0
x = 15
On y intercept x = 0
y = -3.75
Use substitution to solve the system of linear equations. In your final answer, include all of your work.
y = -3x + 4
y + 1/3y = 4/3
The solution is [tex](1,1)[/tex]
Step-by-step explanation:
The system of linear equation is
[tex]y=-3x+4[/tex] and [tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
Using substitution method, let us substitute [tex]y=-3x+4[/tex] in the equation
[tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
[tex]-3 x+4+\frac{1}{3}(-3 x+4)=\frac{4}{3}[/tex]
Multiplying the term [tex]-3x+4[/tex] by [tex]\frac{1}{3}[/tex], we get,
[tex]-3 x+4-x+\frac{4}{3}=\frac{4}{3}[/tex]
Subtracting both sides by [tex]\frac{4}{3}[/tex],
[tex]-3x+4-x=0[/tex]
Simplifying, we get,
[tex]\begin{aligned}-4 x+4 &=0 \\-4 x &=-4 \\x &=1\end{aligned}[/tex]
Now, substitute [tex]x=1[/tex] in [tex]y=-3x+4[/tex]
[tex]y=-3(1)+4\\y=-3+4\\y=1[/tex]
Thus, the solution is [tex](1,1)[/tex]
Answer:
y = -3x + 4
x + 1/3y = 4/3
Substitute the first expression into the second equation for y:
x + 1/3(-3x + 4) = 4/3
x - x + 4/3 = 4/3
4/3 = 4/3
Thus, all real numbers are solutions.
Step-by-step explanation:
HOPE THIS HELPS, GOOD-LCK, and Brainliest, also let me know if i am wrong.
Choose the correct simplification of (3p)(5q).
pq
2pq
8pq
15pq
Answer:15pq
Step-by-step explanation:
The correct expression is 15pq.
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
Expression Definition in MathAn expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division. The terms involved in an expression in math are:
Constant: A constant is a fixed numerical value.
Variable: A variable is a symbol that doesn't have a fixed value.
Term: A term can be a single constant, a single variable, or a combination of a variable and a constant combined with multiplication or division.
Coefficient: A coefficient is a number that is multiplied by a variable in an expression.
Given:
(3p)(5q).
=3p * 5q
=15 pq
Hence, the simplified expression is 15 pq.
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The total temperature change over 3 days in Gritty City was −6 degrees Celsius.
What was the average temperature change each day?
Answer:
-2 degrees celcius
Step-by-step explanation:
-6/3
Answer:
Each day, the temperature rises plus -6 Celsius
Use 10 for m. Then find the value of the expression 3.5m.
Answer:
30
Step-by-step explanation:
the required ans 30 or the valuse is 30
suppose the hot dogs come in packs of 9 and the buns come in packs of 12.it was the least number of each for which this is possible.
Answer:
Step-by-step explanation:
Least common number for 9 and 12 is 36
36/9=4
36/12=3
4 packs of hot dogs and 3 packs of buns
ILL GIVE BRAINLESS AND POINTS.I need step by step explanation
The answer for P(A∪B) is 40/45 (or) 8/9.
Step-by-step explanation:
Given,
The number of students that play only stringed instruments (A) = 35 students.
The number of students that play only brass instruments (B) = 10 students.
The number of students that play both of the instruments = 5 students.
The number of students that play none of the instruments = 5 students.
Probability = Number of required events / Total events
To find the total number of students,
TOTAL = A + B - both + neither.
TOTAL = 35 + 10 - 5 + 5 = 45 students.
P(A∪B) = P(A) + P(B) - P(A∩B)
Probability of A, P(A) = 35 students / 45 students = 35/45
Probability of B, P(B) = 10 students / 45 students = 10/45
Probability of A∩B (both), P(A∩B) = 5 students / 45 students = 5/45
P(A∪B) = (35/45) + (10/45) - (5/45)
= 40/45
P(A∪B) = 8/9
Carmen often orders party trays from her favorite Mexican food restaurant For company events. For a recent company party, she spent $58 on one burrito platter and one taco platter. For a company meeting, she spent $90 on to burrito platters and one taco platter. How much does each type of platter cost?
By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Explanation:To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.
We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.
Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.
Step 1: Establish the Equations
The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.
Step 2: Solve the Equations
From the first equation, we can express T in terms of B: T = 58 - B.
Substitute the expression for T in the second equation: 2B + (58 - B) = 90.Simplify and solve for B: B = 32.Substitute the value of B back into any of the original equations to find T: T = 26.Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Given: F(x) = 3x^2+1, G(x) = 2x - 3, H(X) = x
Find F(x) + G(x) =
[tex]F(x)+G(x)=3x^2+2x-2.[/tex]
Solution:
Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]
To find F(x) + G(x):
Adding two functions which gives another function.
Substitute F(x) and G(x), we get
[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]
[tex]=3x^2+1+2x-3[/tex]
[tex]=3x^2+2x-3+1[/tex]
[tex]=3x^2+2x-2[/tex]
[tex]F(x)+G(x)=3x^2+2x-2[/tex]
Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]
Which of the following describes the graph of y = x² - 7x + 12?
1) The graph has zeroes at x = -4 and x = -3 and it opens downward.
2) The graph has zeroes at x = 4 and x = 3 and it opens downward.
3) The graph has zeros at x = -4 and x = -3 and it opens upward.
4) The graph has zeroes at x = 4 and x = 3 and it opens upward.
Answer:
4
Step-by-step explanation:
its a parabola that opens upward, the zeros are x=4 and x=3
A college with a graduating class of 4000 students in the year 2008 predicts that its graduating class
will grow 5% per year. Write an exponential function to model the number of students y in the graduating class t years
after 2008.
Answer:
[tex]y=4000*(1.05)^t[/tex]
Step-by-step explanation:
The graduating class grows by 5% each year, this means after 1 year the number of students graduating will be 105% of 4000, or
[tex]4000*\frac{105}{100} =4000*1.05[/tex]
And after 2 years it will be
[tex](4000*1.05)*1.05[/tex]
and so on. Thus, after [tex]t[/tex] years the number of students [tex]y[/tex] will be
[tex]\boxed{ y=400*(1.05)^t}[/tex]
An exponential function to model the number of students y in the graduating class t years after 2008 is y = 4000(1.05)^t
Exponential functionsThe standard exponential function is expressed as:
y = ab^x
a is the initial populationb is the rate x is the timeIf a college with a graduating class of 4000 students in the year 2008 predicts that its graduating class will grow 5% per year, hence the required exponential equation will be:
y = 4000(1.05)^t
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In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2
y=-2x+2
y=-1/2x+2
y=-2x+4
y=-1/2x+4
Answer:
y=-1/2x+2
Step-by-step explanation:
y = mx + p
m=slope = -1/2
p= y-intercept = 2
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
The segment for - 2 ≤ x ≤ 2 is a straight line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 1) ← the endpoints of the line
m = [tex]\frac{1-3}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation for - 2 ≤ x ≤ 2
A line passes through the point (4,-7) and has a slope of 3/2. Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
y - y1 = m(x - x1)
slope m = 3/2, y1 = -7, x1 = 4
y + 7 = 3/2(x - 4)
y + 7 = 3x/2 - 6
y = 3x/2 - 6 - 7
y = 3x/2 - 13
Explanation for #4-8
Answer:
Sorry I can't read it :(
Water tower. Model depth 32cm actual depth is ?m
The question involves converting the model depth from centimeters to meters, which typically requires dividing by 100. However, without a specific scale or additional detail, the direct conversion of 32cm would be 0.32 meters.
Explanation:The student's question is about converting the depth of a model water tower, provided in centimeters, to its actual depth in meters without giving a specific depth in the question. This concept usually involves understanding the scale of models and how to apply proportional reasoning to determine actual sizes. However, without a specific scale or the actual depth given in the question, we can't calculate the actual depth.
Generally, to convert from centimeters to meters directly, we divide the length in centimeters by 100, because 1 meter equals 100 centimeters. For example, if a model tower's depth is 32cm, to find this depth in meters, you would divide 32 by 100, which equals 0.32 meters.
It took mr. Raleigh a total of 9 hours to drive to his grandpa’s house. He drove m miles before lunch 240 miles after lunch. If he drove at a constant speed, what expression can be used to find how many miles Mr.Raleigh drove each hour?
What is 2 3/4 • 6 2/3
13. Marisa walked her dog mile on Saturday and 55 mile on Sunday. How far did she walk her dog in all?
Marissa walked her dog 1/10 mile on saturday and 55/100 mile on sunday. how far did she walk her dog in all?
Answer:Marissa walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday
Solution:Given that, Marissa walked her dog
From given information,
[tex]\text{Miles walked on saturday } = \frac{1}{10} \text{ mile }\\\\\text{Miles walked on sunday } = \frac{55}{100} \text{ mile }[/tex]
We have to find the distance walked in all
[tex]\text{Total distance } = \text{Miles walked on saturday + Miles walked on sunday }[/tex]
Substituting the values we get,
[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]
Make the denominators same for easier calculations by taking L.C.M of 10 and 100
Prime factors of 10 = 2 x 2 x 5
Prime factors of 100 = 2 x 2 x 5 x 5
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 5, 5
Multiply these factors together to find the LCM
LCM = 2 x 2 x 5 x 5 = 100
[tex]\text{Total distance } = \frac{1}{10} + \frac{55}{100}[/tex]
[tex]\text{Total distance } = \frac{1 \times 10}{10 \times 10} + \frac{55}{100}\\\\\text{Total distance } = \frac{10}{100} + \frac{55}{100}\\\\\text{Total distance } = \frac{10+55}{100} = \frac{65}{100}[/tex]
Thus she walked [tex]\frac{65}{100}[/tex] miles altogether on saturday and sunday
PLEASEEEE help with #7
Answer:
The answer is B ⅚ because there's only one out of 6 chance that the spinner will land on 6.
I need to solve by completing the square but I just can’t seem to get the correct answer, the quadratic is 2x^2- .5x-28=0
Answer:
x - 5.19 or x = -2.67 is the correct answer.
Step-by-step explanation:
Here, the given quadratic equation is: [tex]2x^2- 5x-28=0[/tex]
To solve it by : Completing The Square
Step : 1 Make the coefficient of leading variable x² as 1.
Divide whole equation by 2,we get:
[tex]x^2- \frac{5}{2} x-14=0\\\implies x^2- \frac{5}{2} x = 14[/tex]
Step 2: Find the coefficient of x in the equation and DIVIDE it by 2 to HALF THE VALUE
Here, the coefficient of x = (-5/2)
Dividing ot by 2, we get the value = (-5/4)
Step 3: ADD THE SQUARE of the found value on BOTH sides.
And USE: [tex](a - b)^2 = a^2 + b^2 - 2ab[/tex]
[tex]x^2- \frac{5}{2} x = 14 \implies x^2- \frac{5}{2} x + (\frac{5}{4} )^2= 14 + (\frac{5}{4} )^2\\\implies (x -\frac{5}{4})^2 = 14 + \frac{25}{16} = \frac{224 + 25}{16} = \frac{249}{16} \\\implies (x -\frac{5}{4})^2 = \frac{249}{16} = (\frac{15.7}{4})^2\\ \implies (x -\frac{5}{4})^2 = (\frac{15.7}{4})^2[/tex]
Step 4: TAKE ROOT ON BOTH SIDES, we get:
[tex](x -\frac{5}{4})^2 = (\frac{15.7}{4})^2\\\implies (x -\frac{5}{4}) = \pm (\frac{15.7}{4})\\\implies x = (\frac{15.7}{4}) +(\frac{5}{4}) = 5.19\\or, x = - (\frac{15.7}{4}) +(\frac{5}{4}) = -2.67\\[/tex]
So, either x - 5.19 or x = -2.67
An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a building is 38°. The engineer knows the building is 300 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot? ✓ 384 ft 487 ft X 234 ft 185 ft
Answer:
My best guess is 384 ft
Step-by-step explanation:
Tangent 38° = opposite side / adjacent side
Tangent 38° = 300 ft / x ft
The value of x from the equation is 383.98 ft. Thus, the engineer is 383.98 ft.
Rounding it up gives us 384 ft.
Answer:
384 ft.
Step-by-step explanation:
We know the opposite side of the triangle and we need the adjacent side.
So tan 38 = opposite / adjacent
= 300 / x
x = 300 tan 38
x = 383.98 feet.