Answer:
38
Step-by-step explanation:
The most occuring number is the mode, which in this case is 38.
Answer: 38
Step-by-step explanation:
The mode of a data set is the number that shows up the most, in this case 38, which shows up 7 times.
Hope it helps <3
If f(x) = squareroot x + 5 and g(x) = -4x + 4,
which statement is true?
Click on the correct answer.
3 is in the domain of fºg.
3 is not in the domain of fºg.
Answer:
3 is not in the domain of [tex]f\circ g[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=\sqrt{x+5}[/tex]
[tex]g(x)=-4x+4[/tex]
We need to check whether 3 is in the domain of [tex]f\circ g[/tex] or not.
[tex]f\circ g=f(g(x))[/tex]
[tex]f\circ g=f(-4x+4)[/tex] [tex][\because g(x)=-4x+4][/tex]
[tex]f\circ g=\sqrt{(-4x+4)+5}[/tex] [tex][\because f(x)=\sqrt{x+5}][/tex]
[tex]f\circ g=\sqrt{-4x+9}[/tex]
This function is defined if
[tex]-4x+9\geq 0[/tex]
[tex]9\geq 4x[/tex]
[tex]\dfrac{9}{4}\geq x[/tex]
It means domain of the function [tex]f\circ g[/tex] is [tex](-\infty,\dfrac{9}{4}][/tex].
[tex]3\notin (-\infty,\dfrac{9}{4}][/tex]
Therefore, 3 is not in the domain of [tex]f\circ g[/tex].
A shoe store marks up the wholesale cost of all shoes they sell by 20%. Calvin wants to buy a pair of shoes that has a price tag of $145. What was the wholesale cost of the shoes?
The sell price is the wholesale price plus 20%
Divide the sell price by 1.2 ( 100% + 20%)
145 / 1.2 = 120.83
The wholesale price is $120.83
Answer:
The wholesale price is $120.83
The Quadratic Formula x =
-btvb2 - 4ac
2a
was used to solve the equation 2x + 10x - 6 = 0. Fill in the missing denominator of the solution.
-5+ 37
Answer:
2
Step-by-step explanation:
I think the answer is 2, because 2a=4, but when simplified, you can divide both the numerator and denominator by 2, making the denominator 4/2= 2.
The missing denominator of the solution is 2.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have,
2x² + 10x -6 = 0
Now, using Discriminant Method
x = [ -b ± √ (b² -4ac)] / 2a
Here, a= 2, b= 10 and c=-6
So, x = [ -10 ± √(10² - 4(2)(-6)] / 2(2)
x = [ -10 ± √ 100 + 48]/ 4
x = (-10 ± 2√37)/ 4
x = (-5 ± √37)/2
Learn more about Equation here:
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A jumbo chocolate bar with a rectangular shape measures 13 centimeters in length, 7 centimeters in width, and 2 centimeters in thickness. Due to escalating costs of cocoa, the management has decided to reduce the volume of the bar by 20 %. To accomplish this reduction, management decides that the new bar should have the same 2 centimeter thickness, but the length and width of each should be reduced by an equal number of centimeters. What should be the dimensions of the new candy bar?
Answer:
Reduce every dimension except thickness by 20%.
The requried new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.
To find the dimensions of the new candy bar after reducing the volume by 20%, we need to determine the reduction in length and width.
Let's start by calculating the original volume of the candy bar using the formula: volume = length × width × thickness.
Original volume = 13 cm × 7 cm × 2 cm = 182 cm³
Since the management wants to reduce the volume by 20%, we need to find 20% of the original volume and subtract it from the original volume.
20% of 182 cm³ = 0.2 × 182 cm³ = 36.4 cm³
Reduced volume = 182 cm³ - 36.4 cm³ = 145.6 cm³
Now, we need to determine the new dimensions while maintaining the 2 cm thickness.
Let's assume the reduction in length and width is x cm for both dimensions.
The new volume can be calculated using the formula:
volume = (length - x) × (width - x) × thickness.
Setting this equal to the reduced volume, we have:
(13 - x) × (7 - x) × 2 = 145.6
Simplifying and rearranging the equation, we get:
(91 - 20x + x²) = 72.8
x² - 20x + 18.2 = 0
Using the quadratic formula, we can solve for x:
[tex]x = \dfrac{-(-20)\pm \sqrt{(-20)^2- 4(1)(18.2)}} {2(1)}\\x = \dfrac{20 \pm \sqrt{400 - 72.8}} {2}\\x =\dfrac {20 \pm \sqrt{327.2}} {2}[/tex]
x ≈ (20 ± 18.09) / 2
Taking the positive value, we have:
x ≈ (20 + 18.09) / 2
x ≈ 19.045 / 2
x ≈ 9.5225
Since the dimensions cannot be negative, we discard the negative value.
Therefore, the reduction in length and width is approximately 9.5225 cm.
To find the new dimensions, we subtract this value from the original length and width:
New length = 13 cm - 9.5225 cm ≈ 3.4775 cm
New width = 7 cm - 9.5225 cm ≈ -2.5225 cm (discard as it is negative)
Therefore, the new dimensions of the candy bar are approximately 3.4775 cm in length, 2 cm in width (maintained), and 2 cm in thickness.
Learn more about dimensions here:
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what is the range of the function?
Answer:
Range { 2,4,9,16}
Step-by-step explanation:
The range of the function is the output of the system
Range { 2,4,9,16}
Answer:
Step-by-step explanation:
Range is ll the y-points the outputs {2,4,9,16}
There are only red,blue and green counters in a bag. There are 6 red counters,4 blue counters and 8 green counters. Matt takes a counter from the bag at random a) What is the probability that the counter is red.Give your answer in a fraction. b) What is the probability that the counter is not blue.Give the answer as a fraction. pls help.
Answer:
a) 1/3
b) 7/9
Step-by-step explanation:
The first part asks for the probability that Matt takes the red counter.
There are 6 red counters out of total 6+4+8 = 18 counters.
6/18
Simplify the fraction.
= 1/3
The second part asks for the probability that the counter is not blue.
The counters that are blue are 4. Not blue becomes 18-4 = 14. 14 red or green counters out of total 18.
14/18
= 7/9
Answer:
Total outcome = 6 + 4 + 8 = 18
a) Probablity that the counter is red = 6/18 = 1/3
b) Probablity that the counter is blue = 14/18 = 7/9
What is (-i)5?
A -1
B 1
C -I
D i
Answer:
-i^5=-i
Step-by-step explanation:
rewrite the equation ;
i^4=1
I^4 *-i = 1*-i=-i
help me please(2 + 3 • 2 + 3²) - 4²
Answer:
1solution,
[tex](2 + 3 \times 2 + {3}^{2} ) - {4}^{2} \\ = (2 + 6 + 9) - 16 \\ = 17 - 16 \\ = 1[/tex]
Hope this helps...
Good luck on your assignment...
Answer:
1
Step-by-step explanation:
Multiply
3 by 2 . 2 + 6 + 3 2 − 4 2 Raise 3 to the power of 2 . 2 + 6 + 9 − 4 2 Raise 4 to the power of 2 . 2 + 6 + 9 − 1 ⋅ 16 Multiply − 1 by 16 . 2 + 6 + 9 − 16
Simplify by adding and subtracting.
Add 2 and 6 . 8 + 9 − 16 Add 8 and 9 . 17 − 16 Subtract 16 from 17 .
1
heleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeep
Answer:
3.625 is ans
Step-by-step explanation:
4.5+0.25_+1.125=3.625
Step-by-step explanation:
this is your answer sis ...
X/5-2=11 what is the solution
Answer:
x=65
Step-by-step explanation:
x/5 - 2 = 11
x/5= 11+2
x/5=13
x=13×5
x=65
Answer:
X = 55 is the answer.Step-by-step explanation:
Question = x/5 - 2 = 11
1. Isolate the variable
x/5 - 2 = 11
+ 2 + 2
x/5 = 11
2. Remove the fraction
x/5 = 11
*5 *5
3. Simplify
x = 55
The answer is x = 55.
Hope this helped,
Kavitha
SOLVE and CHECK the following word problem. (6 marks)
The length of a rectangle is 3 m greater than the width. The perimeter is 38 m. What
are the dimensions of the rectangle?
Answer:
x = 8
Step-by-step explanation:
Let us take the breadth as 'x'
breadth = x
length = 3 + x
perimeter = 38m
perimeter of a rectangle = 2 ( l + b )
= 2( x + x + 3 ) = 38
4x + 6 = 38
4x = 38-6
x = 32/4
x = 8
breadth = 8
length = 11
A portion of the Quadratic Formula proof is shown. Fill in the missing reason. Statements Reasons ax2 + bx + c = 0 Given ax2 + bx = −c Subtract c from both sides of the equation x squared plus b over a times x equals negative c over a Divide both sides of the equation by a x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus the quantity b over 2 times a squared Complete the square and add the quantity b over 2 times a squared to both sides x squared plus b over a times x plus the quantity b over 2 times a squared equals negative c over a plus b squared over 4 times a squared Square the quantity b over 2 times a on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a end quantity squared equals negative 4 times a times c over 4 times a squared plus b squared over 4 times a squared Find a common denominator on the right side of the equation x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation quantity x plus b over 2 times a end quantity squared equals b squared minus 4 times a times c all over 4 times a squared ? Rewrite the perfect square trinomial as a binomial squared on the left side of the equation Take the square root of both sides of the equation Multiply both sides of the equation by 2 Square the left side of the equation
Answer:
Find a common denominator on the right side of the equation
Step-by-step explanation:
I was taking the test and couldn't find the answer to this question anywhere so let me help you out...
abidemiokin provided a wonderful step-by-step explanation for solving the formula, but left out the actual answer for the question which is what I'm here for. I read through abidemiokin's explanation and reviewed my options before choosing the best answer. As you see in step 5 of my edited version of abidemiokin's explanation the missing step is there. In the provided question we see steps 1,2, 3, and 4 being identical to those in the explanation below. From this, it is clear the next step (step 5) would be the next step, and as it is one of the options we can trust that it is correct.
(If you still have doubts then trust the fact that I took the test and the answer I provided above was indeed correct.)
Given the quadratic equation ax²+bx+c = 0, to derive the quadratic formula from the equation, the following steps must be followed;
ax²+bx+c = 0
Step 1: Subtract c from both sides
ax²+bx+c-c = 0-c
ax²+bx = -c
Step 2: Divide both sides of the equation by a
ax²/a + bx/a = -c/a
x² + bx/a = -c/a
Step 3: Complete the square and add the quantity (b/2a)² times a squared to both sides
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
Step 4: Square the quantity b/2a on the right side of the equation
x² + bx/a + (b/2a)² = -c/a + b²/4a²
Step 5: Find a common denominator on the right side of the equation which is 4a²
x² + bx/a + (b/2a)² = -4ac/4a² + b²/4a²
Step 6: Add the fractions together on the right side of the equation
x² + bx/a + (b/2a)² = (-4ac+ b²)/4a²
Note: The fraction at the right-hand side of the equation is to be added together not multiplied as shown in the question.
Step 7: The equation on the left is to be written as a perfect square as shown
(x+b/2a)² = (-4ac+ b²)/4a²
Step 8: Take the square root of both sides
√(x+b/2a)² = √ (-4ac+ b²)/4a²
(x+b/2a) = √(-4ac+ b²)/2a
Step 9: subtract b/2a from both sides
x+b/2a - b/2a = -b/2a + √(-4ac+ b²)/2a
x = -b/2a + √(-4ac+ b²)/2a
Step 10: Add the fractions together on the right-hand side
x = -b±√(-4ac+ b²)/2a
This gives the required equation
Answer: A Find a common denominator on the right side of the equation
Step-by-step explanation: Took the test of FLVS
A small airplane can fly 12 miles in 3 minutes. At this rate, how far can it fly in 7 minutes? In an hour?
Answer:
28 miles in 7 minutes, 240 miles in an hour
Step-by-step explanation:
We can first simplify the rate to miles per minute. Since the plane goes 12 miles in 3 minutes, we can divide it by 3 to find how much it travels in one minute. 12 divided by 3 is 4 and 3 divided by 3 is 1
The plane travels 4 miles a minute
To find how much it travels in 7 minutes, multiply by 7
4x7 is 28
28 miles in 7 minutes
To find an hour, multiply by 60
4x60= 240
240 miles in an hour
Answer the question now fast
Answer:
second and third choice
Step-by-step explanation:
supplamentary = add up to be 180
'15 points in total for brainliest and correct answer, please answer ASAP'
What is the area of the shaded portion if the area of the circle is 56 sq cm?
Answer:
14cm² is the area of the shaded region
Step-by-step explanation:
recognize that those two small triangles plus that arc area is equal to 1/4 of the area of the circle.
56 / 4 = 14cm
2. Below is a circle with centre C. A, B, D, and E
are points on the circumference. BD is a diameter of
the circle.
Angle CDA is 18° Find the size of angle EDA.
You must show your workings
Answer:
Step-by-step explanation:
45-37
8x17 = 136
)Bentley had $40 in birthday money in her piggy bank. She spent $10 on new flip-flops, then got $20 for her allowance and did not spend any of that money for 1 week. Finally, she spent $15 on new sunglasses. Which part of the scenario is best represented by a linear increasing interval? Bentley has $40 in her piggy bank. Bentley spent $10 on new flip flops. Bentley got $20 for her allowance. Bentley spent $15 on sunglasses.
Answer:
Bentley got $20 for her allowance.
Step-by-step explanation:
Which of the following is a solution of the system
x - 2y < 4 and y > – 2x – 5?
1. (1, - 4)
2. (-8,2)
3. (0,0)
4. (-3,0)
Answer:
Answer B
Step-by-step explanation:
1. (1, -4) is NOT a solution because (1) - 2(-4) < 4 is false.
2. (-8, 2): -8 - 2(2) < 4 is true, and in simplified form is -12 < 4 (true) We must check whether this point (-8, 2) ALSO satisfies y > -2x - 5:
2 > -2(-8) - 5. Yes, this is true, so the given point satisfies both inequalities in Answer B.
Cecilia made an envelope to mail a letter. She colored the regular trapezoid flap on the bottom of the envelope blue, as shown. What is the area of the blue flap of the envelope? 14 Inches squared 18 Inches squared 45 Inches squared 90 Inches squared
Answer:
The correct option is:
14 inches
Step-by-step explanation:
The question is incomplete because the picture of the flap is not shown in the question nor the measurements are given. First lets complete the question. The figure was this question is attached below.
We can see that the bottom width of the trapezoid is 9 inches, the top width of the trapezoid is 5 inches, and it has a height of 2 inches.
The area of trapezoid is given as:
Area = ((Top width + Bottom width)/2) · h
Area = ((9+5)/2) · 2
Area = (14/2) · 2
Area = 7 · 2
Area = 14 inch²
Answer:
14
Step-by-step explanation:
Ordered pair for this point? (The point is circled in Blue)
Answer:
( -3, 1)
........
Answer:
(-3, 1)
Step-by-step explanation:
The point lies on the line x = -3.
The point lies on the line y = 1.
Where both lines intersect, that is the coordinate.
(x, y)
(-3, 1)
What is the product of Three-fourths and Negative StartFraction 6 over 7 EndFraction?
Negative StartFraction 7 over 8 EndFraction
Negative StartFraction 9 over 14 EndFraction
StartFraction 9 over 14 EndFraction
Answer:
[tex]-\frac{9}{14}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}*-\frac{6}{7}\\\\\frac{3}{2} *\frac{3}{7} \leftarrow \text{Cross Cancel Common Factor}\\\\ -\frac{3*3}{2*7}\\\\-\frac{9}{14}[/tex]
Answer:
negative 9/14
Step-by-step explanation:
Please answer I’m not good with math
Answer: A
Step-by-step explanation:
it's easy
Complete the equation of the line through (-6,-5) (−4,−4) PLZ HELP !!!
Answer: y=1/2x−2
Step-by-step explanation:
Which is a valid prediction about the continuous function
f(x)?
f(x) < 0 over the interval (-00, 0).
f(x) > 0 over the interval (-1,00).
f(x) > 0 over the interval [-1, 1].
f(x) < 0 over the interval (0, 2).
pls hurry
Answer:
Option C.
Step-by-step explanation:
Note: In option C interval should be (-1,1) instead of [-1,1].
From the given table it is clear that the value of f(x) is 0 at x=-1 and x=1.
The value of f(x) is negative over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]. So,
[tex]f(x)<0[/tex] over the interval [tex](\infty,-1)\text{ and }(1,\infty)[/tex]
The value of f(x) is positive over the interval [tex](-1,1)[/tex]. So,
[tex]f(x)>0[/tex] over the interval [tex](-1,1)[/tex]
Therefore, the correct option is C.
6. At a bus interchange, a number of passengers boarded a bus. At the first
bus stop, of the passengers alighted the bus and 6 people boarded the
bus. At the 2nd bus stop, of the passengers alighted and 10 passengers
boarded the bus. There were 24 passengers on the bus when it left the
2nd bus stop. How many passengers boarded the bus at the interchange?
Answer:
The answer is given below
Step-by-step explanation:
Let the number of passengers that boarded the bus at the interchange be x.
At the first bus stop, 1/4 of the passengers alighted the bus and 6 people boarded the bus.
Therefore The number of passengers when the bus left the first bus stop = [tex]x-\frac{1}{4}x +6=\frac{3}{4}x+6[/tex]
At the 2nd bus stop, 8/15 of the passengers alighted and 10 passengers boarded the bus.
Therefore The number of passengers when the bus left the second bus stop
[tex]=\frac{3}{4}x+6-\frac{8}{15}( \frac{3}{4}x+6)+10=\frac{3}{4}x+6-\frac{8}{20}x-3.2+10\\\\=\frac{7}{20}x+12.8[/tex]
Given that there were 24 passengers on the bus when it left the 2nd bus stop
[tex]\frac{7}{20}x+12.8=24\\7x+256=480\\7x=480-256\\7x=224\\x=32[/tex]
Therefore 32 passengers boarded the bus at the interchange
What is the distance between the points (-3, 9) and (5, 1)? Round to the
nearest tenth, if necessary.
Answer: 11.3
Step-by-step explanation:
To find the distance, we will need the distance formula.
[tex]D=\sqrt{(x_{2}-x_{1} ) ^2+(y_{2}-y_{1})^2 }[/tex]
Since we know our x and y, we can plug them into this equation.
[tex]D=\sqrt{(5-(-3))^2+(1-9)^2}[/tex]
[tex]D=\sqrt{(8)^2+(-8)^2}[/tex]
[tex]D=\sqrt{64+64}[/tex]
[tex]D=\sqrt{128}[/tex]
[tex]D=11.3[/tex]
The distance between the points is 11.3.
HELP ME PLEASE 10 POINTS ON IT PLEASE HELP ASAP WITH EXPLANATION PLEASE
a) 382 mm
b) 505 mm
c) 3162 mm
d) 3103 mm
e) 5008400 mm
f) 9046850 mm
basically, there are 10mm in a cm, so you times by ten,
1000mm in a m so multiply by 1000
1000000mm in a km
PLZ HELP!! HURRY!!!30POINTS!!
Answer & Step-by-step explanation:
What number is represented by point B?
Which point represents the number 2?
Answer:
-1, c
Step-by-step explanation:
Each dot represents 1.
0 - 1 = -1
As labeled, c represents 2.
Determine the magnitude of the difference of the following vectors: 7-7
ū=77 - 127
v=-21 +7
12.08
a.
C.
14.21
b. 13.83
d.
15.81
Hi there! Let’s see if I can help you <3
The Answer is: 15.81!
Here’s the step by step explication:
First we must find the difference of U and V: (7i-12j)-(-2i+j)
Distributed all out will equal: 9i-13j
We can then go ahead and use Pythagorean therm to find the magnitude: V = Square root of (9)^2 + (-13)^2
This equals Square root of 250!
Depending on the form your teacher wants to answer in it would finally be 5 square roots of 10 or in decimal form; approximately 15.8114!
HOPE IT HELPED YOUUU <3