The number of mangoes = 48
The number of grapefruit = 12
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A box of fruit has four times as many oranges as grapefruit.
And, Total number of fruit = 60 pieces
Now,
Let number of grapefruit = x
Then, Number of Mangoes = 4x
So, We can formulate;
⇒ x + 4x = 60
Solve for x as;
⇒ 5x = 60
⇒ x = 12
Thus, Number of grapefruit = x
= 12
Then, Number of Mangoes = 4x
= 4 × 12
= 48
Therefore, The number of mangoes = 48
The number of grapefruit = 12
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Which equation represents the total commission (c) a sales associate receives if he sells laptop computers (l) with a commission of $39.95 for each sold laptop? What's the total commission if he sells 15 laptops?
A)
l = 39.95c; $599.25
B)
c = 39.95l; $2.66
C)
l = 39.95c; $2.66
D)
c = 39.95l; $599.25
Answer:
D
Step-by-step explanation:
The total commission is the number of laptops times the commission per laptop. Thus, [tex]c=39.95l[/tex].
Setting [tex]l=15[/tex], [tex]c=39.95(15)=599.25[/tex].
A building is constructed using bricks that can be modeled as right rectangular prisms with a dimension of 8in by 2 3/4 by 2 3/4.If the bricks cost $0.06 per cubic inch, find the cost of 850 bricks. Round your answer to the nearest cent.
Given the building that can be modeled as a
right rectangular prism with dimentions
8 * 2 3/4 * 2 3/4
Volume is given by
[tex]V=8*2\frac{3}{4}*2\frac{3}{4}[/tex][tex]V=8*2\frac{3}{4}*2\frac{3}{4}[/tex][tex]V=60.5in^3[/tex]since we have 850 bricks
the volume occupied by 850 bricks is therefore
[tex]Vbricks=60.5*850[/tex][tex]Vbricks=60.5*850[/tex][tex]Vbricks=51425[/tex]then
the cost of the 850 bricks is
[tex]Cbricks=51425*0.06[/tex][tex]Cbricks=3085.5[/tex]cost of bricks is $3085.50
can someone please help me i don't understand this
Answer:
Step-by-step explanation:
equation of finding a midpoint is (x2+x1)/2 and (y1+y2)/2
7) (4+12)/2 = 8 and (9+-4)/2= 2.5
hence midpoint is (8,2.5)
8) we are told the midpoint so we can now find the co-ordinates of the other endpoint:
(5+x)/2= -3
rearrange to find x--> 5+x =-6, so x=-11
(-7+y)/2=2
rearrange to find y--> -7+y=4, so y=11
other endpoint: (-11,11)
5) the gradient of the new equation is parallel to y=3x+7 so it will stay the same
y=3x+c
we know that the points this line passes through is: (-4,-8) so we substitute this into our new equation to find c
-8= (3 x -4) +c
-8=-12 +c
so c= 4
Hence our new equation is y=3x+4
6) perpendicular gradient means that our existing gradient needs to be reciprocated (turned into negative and then flipped)
new gradient is -1/3
y=-1/3x+c
we know the value for x and y so we can substitute into our new equation to find c
9=(-1/3 x -6) +c
9=2 + c
c= 7
Hence our new equation is y=-1/3x+7
Hope this helps!
Simplify: 3 3/9+2 10/18
The answer of the given fraction after simplification is 2.11.
Define simplification.To simplify simply means to make anything easier. Simplifying an equation, fraction, or issue in mathematics entails taking something complex and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common components from the numerator and the denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given fraction is:
= 3 * 3/9 + 2 * 10/18
By simplifying the given fraction, we get
= 3 * 1/3 + 10/9
= 1 + 1.11
= 2.11
The answer of the given fraction after simplification is 2.11.
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Factor the expression 36a + 42b - 18a + 6
+10 points=brainliest
Answer:
6(3a+7b+1)
Step-by-step explanation:
36a+42v-18a+6
18a+42b+6
GCF=6
6(3a+7b+1)
The factor of the given expression is 6(3a+7b+1).
What are factors?A factor is a number that divides another number, leaving no remainder.
Given an expression, 36a + 42b - 18a + 6
On factoring, we get,
36a + 42b - 18a + 6
= 18a+42b+6
= 6(3a+7b+1)
Hence, The factor of the given expression is 6(3a+7b+1).
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The radius of a cylindrical water tank is 6.5 ft, and its height is 12 ft. What is the volume of the tank? Use the value 3.14 for T, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer. Continue 6.5 ft 12 ft 0 K ft X ft² 5 ft3 ?
Solution:
The volume of a cylinder is expressed as
[tex]\begin{gathered} volume=\pi r^2h \\ where \\ r\Rightarrow radius\text{ of its circular end} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]Given the cylindrical water tank below:
where
[tex]\begin{gathered} r=6.5\text{ ft} \\ h=12\text{ ft} \\ \pi=3.14 \end{gathered}[/tex]By substitution, we have
[tex]\begin{gathered} volume\text{ = 3.14}\times(6.5)^2\times12 \\ =1591.98 \\ \Rightarrow volume\approx1592\text{ ft}^3\text{ \lparen nearest whole number\rparen} \end{gathered}[/tex]Hence, the volume of the cylindrical water tank, to the nearest whole number, is
[tex]1592\text{ ft}^3[/tex]Finding the final amount in a world power problem on a compound interest
Using the compound interest formula, we have:
[tex]FV=2000(1+\frac{0.12}{2})^{6\cdot2}[/tex][tex]FV=2000(1.06)^{12}[/tex][tex]FV\approx4024.39[/tex]HELPPPP PLSSSS I NEED A STEP BY STEP
Answer:
see explanation
Step-by-step explanation:
If the ratios of two pairs of corresponding sides of the 2 triangles are equal and the included angles are congruent then the triangles are similar by the
SAS postulate.
[tex]\frac{AC}{DF}[/tex] = [tex]\frac{5.1}{1.7}[/tex] = 3
[tex]\frac{BC}{EF}[/tex] = [tex]\frac{3.3}{1.1}[/tex] = 3
∠ C = 180° - (36 + 67)° = 180° - 103° = 77° , then the included angles
∠ C and ∠ F = 77° are congruent
Then
Δ ABC and Δ DEF are similar by the SAS postulate
.A jar contains 15 green marbles numbered 1 through 15 and 9 red marbles numbered 1 through 9. A marble isdrawn at random from the jar. Find the probability that the marble is green or even numbered.
Answer: 19/24
Explanation:
From the information given,
Number of green marbles = 15
Number of red marbles = 9
Total number of marbles = 15 + 9 = 24
Probability is expressed as
number of favorable outcomes/number of total outcomes
Probability f selecting a greeen marble = 15/24
Even numbers divide 2 without a remainder. The even numbered marbles are
red = 2, 4, 6, 8
green = 2, 4, , 68, 10, 12, 14
Total number of even numbered marbles = 11
Probability of selecing an oevennumber = 10124
The events are not mutually exclusive becuse they can occur together. For two ebvents, A and B that are not mutually exclusive,
P(A U B) = P(A) + P(B) - P(A and B)
Thus,
the probability that the marble is green or even numbered = Probability of selecting a green marble + Probability of selecting an even number - Probability of selecting a green and even numbered marble
Number of green even numbere marble s = 7
Probability of selecting a green and even numbered marble = 7/24
Thus,
the probability that the marble is green or even numbered = 15/24 + 11/24 - 7/24
the probability that the marble is green or even numbered = 19/24
Which of the following is a factor of x³ + 343?
x-7
x² - 14x + 49
x² + 7x +49
x+7
Answer:factor of x³ + 343
Step-by-step explanation: Option D is correct. A factor of an expression is usually referred to as a number or an algebraic expression that divides the known expression. The above algebraic expression needs to be expanded to determine its factor; Mathematically; x³ + 343 = (x + 7) (x² - 7x + 49) Therefore, we can conclude that the factors are (x + 7) (x² - 7x + 49)
the diagram shows a sector of a circle, center O. The radius of the circle is 6cm. angle AOB is 120. work about the perimeter of the sector.
picture below:
The perimeter of the sector is 2cm
The diagram shows a sector of a circle, center O.
The radius of the circle is 6cm.
The angle AOB is 120
We need to find the perimeter of the sector
s = r∅
Where ∅ is the angle subtended by the arc
r is the radius of the circle
s = 6 (120/360)
s = 6 (1/3)
s = 2
Therefore, the perimeter of the sector is 2cm
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select the correct location on the graph PICTURE OF PROBLEM AND GRAPH BELOW
Given the graphed equation:
[tex]0.01x^3-3=|x|-5[/tex]Let's determine the point that represents a negative solution for x.
The solutions are the points where both lines meet.
From the graph, the solution which has a negative solution for x is:
(-2, -3)
In this point of intersection, the value of the x-coordinate is -3 (which is a negative value).
Therefore, the point which represents a negative solution for x is:
(-2, -3)
ANSWER:
(-2, -3)
What is the answer we need the answer
To earn exactly $252, madison needs to work for 21 hours.
Time money
worked earned
5 60
8 96
12 144
15 180
We need to find how many hours should madison work to earn exactly $252
For 5 hours she earns $60
So in 1 hour she earns $ 60/5 = 12
For $1 she needs to work for 1/12 hour
For 252 she need to work for (1/12) 252
For 252 she need to work for 21
Therefore, to earn exactly $252, madison needs to work for 21 hours.
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[{12 - 6 (5 - 3) + 2} + 5 (6-71]
Here, we want to evaluate the expression
We use the order of operations here PEDMAS ( parentheses, exponents (roots and powers) , division, multiplication, addition and subtraction)
We start out with the parentheses, then move on with the terms outside by multiplication
We have this as follows;
[tex]\begin{gathered} ((12\text{ -6(2)+2)) + 5(-65))} \\ =\text{ ((12-12+2)-325)} \\ =\text{ 2-325 = -323} \end{gathered}[/tex]How many deciliters are in 1 milliliter?100100.10.01
We are asked to find how many deciliters can be found in 1 mililiter.
To get the solution we have to find the conversion factor. All we need to do is divide the volume by 100.
Here is a formula
[tex]\text{Value in deciliters =}\frac{Value\text{ in mililiters}}{100}[/tex]This implies,
[tex]\begin{gathered} \text{Value in deciliters=}\frac{1}{100} \\ \text{Value in deciliters}=0.01 \end{gathered}[/tex]ANSWER: 0.01
Graph the function by first finding the relative extrema. f(x) = x3 + 4x2 - X - 4 $ HI 4 M 2 4 a 2 4 2 WHATS
The relative extrema of the function f(x) = x³ + 4x² - x - 4 is at
( [tex]-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27}[/tex] )and the graph of the function is attached below.
The given function is f(x) = x³ + 4x² - x - 4
For the relative extrema we will first have to find the first derivative of the function:
f'(x) = 3x² + 8x - 1
Now for4 the function to have an extremum, f'(x) = 0
3x² + 8x - 1 = 0
Solving we get :
the values of x using the quadratic formula are [tex](-\frac{4-\sqrt{19}}{3} , -\frac{4+\sqrt{19}}{3} )[/tex] .
Now we will substitute the values of x in the function f(x) to get the local extremum.
The maximum value of f(x) is [tex]\frac{56+38\sqrt19}{27}[/tex].
The minimum value of f(x) is [tex]\frac{56-38\sqrt19}{27}[/tex] .
Now we will use various points to find the values of f in the function.
At x = -3 , y = 8
At x = 0 , y = -4
At x =-1 , y = 0
Hence the relative extremum of the function is at [tex](-\frac{4+\sqrt{19}}{3} ,\frac{56+38\sqrt19}{27})[/tex] .
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9.3 divided by 3.8 HELP ME
Answer:
Step-by-step explanation:
0 0. 4 0
9 3 3 8. 0 0
− 0
3 8
− 0
3 8 0
− 3 7 2
8 0
− 0
8 0
0.40
2.45 is the answer to 9.3 divided by 3.8
In a college there are 16 times as many students as professors. If together the students and professors number 42,500, how many students are there in the collego?The number of students in the college is
Let the number of professors be x.
If there are 16 times as many students as professors, then the number of students will be:
[tex]x\times16=16x[/tex]If the number of students and professors is 42,500, then we have that:
[tex]\begin{gathered} x+16x=42500 \\ 17x=42500 \end{gathered}[/tex]Solving by dividing both sides by 17, we have:
[tex]\begin{gathered} x=\frac{42500}{17} \\ x=2500 \end{gathered}[/tex]Hence, we can calculate the number of students in the college to be:
[tex]\Rightarrow2500\times16=40000[/tex]Therefore, there are 40,000 students in the college.
The piston diameter of a certain hand pump is inch. The manager determines that the diameters are normally distributed, with a mean of inch and a standard deviation of inch. After recalibrating the production machine, the manager randomly selects pistons and determines that the standard deviation is inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the level of significance?.
We fail to reject the null hypothesis and there is no significant evidence for the manager to conclude that the standard deviation has decreased at the α = 0.01
What is standard deviation?
The standard deviation is a statistic that expresses the degree of variation or dispersion among a group of data. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the mean of the collection.
The null and alternative hypotheses are:
[tex]H_{0} :[/tex] α = 0.004
[tex]H_{a} :[/tex] α < 0.004
Under null hypothesis, the test statistic is:
[tex]x^{2} = \frac{(n-1)s^{2} }{\alpha ^{2} }[/tex]
= (29 - 1)0.0036² / 0.004²
= 22.68
Now the critical value of x² at 0.01 level of significance for
df = n-1
= 29 - 1
= 28
[tex]x_{critical} ^{2}[/tex] = 48.278
Since the test statics
x² = 22.68 is less than the critical value
[tex]x_{critical} ^{2}[/tex] = 48.278
∴ we fail to reject the null hypothesis and there is not significant evidence for the manager to conclude that standard deviation has decreased at α = 0.01
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Divide £350 in the ratio
3:11
£350 is divided in the ratio 3:11 is £75 and £275.
The given ratio is 3:11.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
We need to divide £350 in the given ratio
Now, 3+11=14
3/14 × 350
= £75
11/14 × 350
= £275
Hence, £350 is divided in the ratio 3:11 is £75 and £275.
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2A professional pyro technician shoots fireworks vertically into the air from the ground with an initial velocity of 192
feet per second. The height in feet of the fireworks is given by h(t) = -16t² + 192t.
a. How long does it take for the fireworks to reach the maximum height?
b. What is the maximum height reached by the firework?
Answer:
See below
Step-by-step explanation:
Maximum height will be found at the t value = - b/2a
b = 192 a = -16
so max height will be at t = - 192/(2 * -16) = 6 s
Max height will be h = -16(6^2) + 192(6) = 576 ft
Which of the following ratios are equivalent to 8:2?
A 16:4
B 40:10
C 2:8
D 10:4
E 1:6
F 4:1
Answer:
A, B, F
Step-by-step explanation:
Well, to do this let's start by simplifying each of the ratios! If they can be simplified to 8:2 then they are a match
A: 16:4
Divide both sides by 2: 8:2 (This is an answer)
B: 40:10
Divide both sides by 5: 8:2 (This is also an answer)
C: 2:8
This one is not possible, because you would have to multiply the 2 by a whole number, and the 8 by a number less than one. Both have to be multiplied/divided by the same number.
D: 10:4
To get the 4 into a 2, we divide by 2. If we divide the 10 by 2 we get 5. Thus, this is not an answer.
E: 1:6
To get the 6 into a 2, we must divide it by 3. If we divide 1 by 3, we get a decimal, not 8.
F: 4:1
Multiply both sides by 2: 8:2 (This is our final answer)
How to calculate the volume of this shape?
(1 litre = 1000 cm^3)
Answer:
it is half of volume of tube.
tube volume = area of circle (πr)× height of tube (h)
volume of tube = π × r × t
1/2 tube volume = 1/2 × π × r × h
PLS HELP ILL MATK BRAINLIEST
the area of a square garden is
84 square
feet what is the best estimate of the sidelenght of the garden
21
11
7
9
Answer:
40q7572928254949262618394938282920420
identify the term in experimentation -2X
The given expression is
[tex]-2x^8+3x^2-x+11[/tex]Terms are the expressions separated by negative or positive signs. In this case, there are 4 terms.
Coefficients are the number multiplying the variable. IN this case, the coefficients are -2, 3, and -1.
The variable is just x because it's the only letter present in the expression.
The powers are x'8 and x'2.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
What are the factors of the following quadratic?x2 + 9x + 8
we have
x2 + 9x + 8
Find the factors
Complete the square
(x^2+9x+81/4)-81/4+8=0
Rewrite as perfect squares
(x+9/2)^2=81/4-8
(x+9/2)^2=49/4
square root both sides
(x+9/2)=(+/-)7/2
x=-9/2(+/-)7/2
so
x1=-9/2+7/2=-1
x2=-9/2-7/2=-8
therefore
x2 + 9x + 8=(x+1)(x+8)
answer is
The factors are
(x+1) and (x+8)
At a sale this week, a suit is being sold for $145.60. This is a 74% discount from the original price. What is the original price?
$145.60 ---> 74%
x -------------> 100%
[tex]\begin{gathered} x\times74=145.60\times100 \\ 74x=14560 \\ \frac{74x}{74}=\frac{14560}{74} \\ x=196.76 \end{gathered}[/tex]answer: $196.76 is the orginal price
Juan had $3.50. Julian had 2 1/2 times as much as juan how much money did julian have
A. "Describe the trend in vehicle sales over time" - Should I use a regression model or just a linear model?
Regression
A) We can see the graph and through the data that the most indicated form is to find the regression model since there is not much uniformity among the data to describe it as a purely linear model.
Plotting that scatterplot, and generating the equation we know that the equation is:
[tex][/tex]