Answer:
22
Step-by-step explanation:
22 shows up twice and the rest of the numbers show up once.
Answer:22
Step-by-step explanation:
It appears most often.
You and your friend each collect rocks and fossils. Your friend collects three times as many rocks and half as many fossils as you. You collect 20 objects. Your friend collects 20 objects. How many rocks and how many fossils do you each collect?
Answer:
I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.
Step-by-step explanation:
The number of total objects collected by me = 20
The number of objects collected by my friend = 20
Let us assume:
The number of rocks collected by me = m
The number of fossils collected by me = 2 k
⇒ m + 2 k = 20 .... (1)
So, according to the question:
The number of rocks collected by my friend = 3 x (rocks collected by me)
= 3 x (m) = 3 m
The number of fossils collected by my friend = 1/2 x (fossils collected by me) = 1/2 x (2k ) = k
⇒ 3 m + k = 20 .... (2)
Solving (1)and (2) for the value of m and k, we get:
m + 2 k = 20 ⇒ m = 20 - 2 k ... Put this in (2)
3 m + k = 20 ⇒ 3 (20 - 2 k) + k = 20
⇒ 60 - 6 k + k = 20
or, - 5k = -40
or, k = 40/5 = 8
⇒ k= 8
m + 2(8) = 20
or, m = 4
Hence, the number of rocks collected by me = m = 4
The number of fossils collected by me = 2 k = 2 (4) = 16
Hence, the number of rocks collected by my friend = 3 m = 3 x 4 = 12
The number of fossils collected by my friend = k = 8
Hence, I collect 4 rocks and 16 fossils. While my friend collects 12 rocks and 8 fossils.
You collect 4 rocks and 16 fossils. Your friend collects 12 rocks and 8 fossils.
You and your friend each collect 20 objects. Let's define our variables:
Let R represent the number of rocks you collect. Let F represent the number of fossils you collect.
Your Collection:You collect 20 objects in total:
R + F = 20
Your Friend's Collection:Your friend collects three times as many rocks and half as many fossils as you:
Rocks: 3R Fossils: F / 2
Your friend also collects 20 objects in total:
3R + F / 2 = 20
Solve the EquationsWe have two equations:
R + F = 20 and 3R + F / 2 = 20
First, solve equation 1 for F:
F = 20 - R
Next, substitute this into equation 2:
3R + (20 - R) / 2 = 20
Multiply everything by 2 to clear the fraction:
6R + 20 - R = 40
Simplify:
R + 20 = 40
Subtract 20 from both sides:
5R = 20
Divide by 5:
R = 4
Now, substitute R back into the equation for F:
F = 20 - 4
F = 16
Then, 3R= 12 and F/2 = 8
Thus, you collect 4 rocks and 16 fossils. Your friend collects 12 rocks and 8 fossils.
How to solve this equation of the missing sides of the triangle
Step-by-step explanation:
Given is a 45°-45°-90 ° angled triangle.
By 45°-45°-90 ° angled triangle theorem:
side opposite to 45° angle is [tex] \frac{1}{\sqrt 2} [/tex] times of hypotenuse.
[tex] \therefore \: 7 = \frac{1}{ \sqrt{2} } \times m \\ \\ \huge \red{ \boxed{\therefore \: m \: = 7 \sqrt{2} \: units}} \\ \\ n \: = \frac{1}{ \sqrt{2} } \times m \\ \\ \therefore \:n \: = \frac{1}{ \sqrt{2} } \times 7 \sqrt{2} \\ \huge \purple{ \boxed{\therefore \:n \: = 7 \: units}} \\ [/tex]
Tony is at a car rental service to rent a car. There is an administration fee of $50 to rent a car and then it costs $20 for each day he has the car. Write an expression for the total
cost of renting a car at this particular car rental service.
Answer:
20x+50
Step-by-step explanation:
Let x represent the number of days he has the car
20x+50
It is 20x, because it costs 20 dollars for each day he has the car, and +50, because there is a fee, regardless of how many days he has the car.
Hope this helps!
What is -x^2 if x=-2
Answer:
-4
Step-by-step explanation:
plug in -2
-(-2)^2 = -4
4. You substitute the x with -2, which means the problem is -(-2^2).
- Write each expression as a multiple of a power of 10:
a. 0.04
b. 0.072
c. 0.0000325
d. Three thousandths
e. 23 hundredths
f. 729 thousandths
g. 41 millionths
Answer:
To write the following expressions as a multiple of a power of 10 you need to take each of the numbers and raise them to the power of 10.
An easy way to do this is to find the decimal point and move it over one spot to the right.
a. 0.04- move the decimal one to the right and you get that 0.04^10=00.4.
b. 0.072-move the decimal to the right one spot you get 0.072^10=00.72.
c. 0.0000325-move your decical to get 0.0000325^10=00.000325.
d. 0.003-move the decimal to get 0.003^10=00.03 or three hundredths.
e. 0.23-move your decimal to get 0.23^10=2.3 or two and three tenths.
f. 0.729-move you decimal to the right to get 0.729^10=07.29 or seven and twenty-nine hundredths.
g. 0.000041- move your decimal to the right to get 0.000041^10=00.00041 or forty-one hundred thousandths.
Hope this helps ;)
To write the expression as a multiple of a power of 10 ; we express the decimals in scientific notation :
0.04 :
Two decimal points to the left ;0.04 = [tex] 4 \times 10^{-2}[/tex]
0.072 :
3 decimal points to the left ;0.072 = [tex] 7.2 \times 10^{-3}[/tex]
0.0000325 :
Two decimal points to the left ;0.04 = [tex] 3.25 \times 10^{-5}[/tex]
Three thousandth = 0.003 :
3 decimal places to the left0.003 = [tex] 3 \times 10^{-3}[/tex]
23 hundredths = 0.023:
2 decimal places to the left0.023 = [tex] 2.3 \times 10^{-2}[/tex]
729 thousandths = 0.00729 :
3 decimal places to the left0.00729 = [tex] 7.29 \times 10^{-3}[/tex]
41 millionths = 0.0000041
6 decimal places to the left0.0000041 = [tex] 4.1\times 10^{-6}[/tex]
Hence, the scientific representation.
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The floor of a domed camping tent measure 7 feet by 9 feet. What is the area of the floor of the tent?
Answer:
63ft
Step-by-step explanation:
area=basexheight so 7x9 which is 63
The dDifference in hours between full times and the part timers to work three hours a day is 2 working hours how many hours per day to full timers work
full timers work 5 hours a day whereas Part timers work 3 hours a day!
Step-by-step explanation:
Here we have , The difference in hours between full times and the part timers to work three hours a day is 2 working hours . We need to find that how many hours per day to full timers work . Let's find out:
Let full timers work x hours , Part time workers work 3 hours a day , According to question, difference in hours between full times and the part timers to work three hours a day is 2 working hours i.e.
⇒ [tex]x-3 = 2[/tex]
Adding 3 to make x term alone :
⇒ [tex]x-3+3 = 2+3[/tex]
⇒ [tex]x=5[/tex]
Therefore, full timers work 5 hours a day whereas Part timers work 3 hours a day!
1. Bob is looking to buy a new baseball cap with his favorite team’s logo on it. He finds one that normally sells for $32. If a 7% sales tax is added, what is the total cost?
(Find with percent equation)
Answer:
The total cost is $34.24.
Step-by-step explanation:
Given : Bob is looking to buy a new baseball cap with his favorite team’s logo on it. He finds one that normally sells for $32. If a 7% sales tax is added.
To find : What is the total cost?
Solution :
The sales price = $32
The tax rate = 7%=0.07
The sales tax is given by,
[tex]\text{Sales tax}=\text{Rate}\times \text{Price}[/tex]
[tex]\text{Sales tax}=0.07\times 32[/tex]
[tex]\text{Sales tax}=2.24[/tex]
Now, adding to sales price
Total cost = 32+2.24
Total cost = $34.24
Therefore, the total cost is $34.24.
Point P' is the image of P(5,-5) under a translation by 2 units to the left and 5 units up.
What are the coordinates of P'?
Answer:
The coordinates of [tex]P^\prime[/tex] would be [tex](3,\, 0)[/tex].
Step-by-step explanation:
The two points [tex]P[/tex] and [tex]P^\prime[/tex] are on a Cartesian plane.
By convention, the positive [tex]x[/tex]-axis on a Cartesian plane points to the right. As a result,
Moving a point to the right by [tex]a[/tex] units is the same as adding [tex]a[/tex] to its [tex]x[/tex]-coordinate. If the point was initially at [tex](x_0,\, y_0)[/tex], it would be moved to [tex](x_0 + a,\, y_0)[/tex].Moving a point to the left by [tex]a[/tex] units is the same as subtracting [tex]a[/tex] from its [tex]x[/tex]-coordinate. If the point was initially at [tex](x_0,\, y_0)[/tex], it would be moved to [tex](x_0 - a,\, y_0)[/tex].Also by convention, the positive [tex]y[/tex]-axis on a Cartesian plane points upwards. Similarly,
Moving a point upwards by [tex]b[/tex] units is the same as adding [tex]b[/tex] to its [tex]y[/tex]-coordinate. If the point was initially at [tex](x_0,\, y_0)[/tex], it would be moved to [tex](x_0,\, y_0 + b)[/tex].Moving a point downwards by [tex]b[/tex] units is the same as subtracting [tex]b[/tex] from its [tex]y[/tex]-coordinate. If the point was initially at [tex](x_0,\, y_0)[/tex], it would be moved to [tex](x_0,\, y_0 - b)[/tex].In this case,
Point [tex]P[/tex] was initially at [tex](5, -5)[/tex].[tex](5, -5)[/tex] is at [tex](5 - 2, \, -5)[/tex] after it is moved to the left by [tex]2[/tex] units. That's the same as [tex](3,\, -5)[/tex].[tex](3,\, -5)[/tex] is at [tex](3,\, -5 + 5)[/tex] after it is moved upward by [tex]5[/tex] units. That's the same as [tex](3,\, 0)[/tex].Therefore, the coordinates of [tex]P^\prime[/tex] would be [tex](3,\, 0)[/tex].
Answer:
(3,0)
Step-by-step explanation:
The two points and are on a Cartesian plane. By convention, the positive -axis on a Cartesian plane points to the right. As a result,Moving a point to the right by units is the same as adding to its -coordinate. If the point was initially at , it would be moved to .Moving a point to the left by units is the same as subtracting from its -coordinate. If the point was initially at , it would be moved to .Also by convention, the positive -axis on a Cartesian plane points upwards. Similarly, Moving a point upwards by units is the same as adding to its -coordinate. If the point was initially at , it would be moved to .Moving a point downwards by units is the same as subtracting from its -coordinate. If the point was initially at , it would be moved to .In this case, Point was initially at . is at after it is moved to the left by units. That's the same as . is at after it is moved upward by units. That's the same as .Therefore, the coordinates of would be .
Tell whether the expression is positive or negative without evaluating.
1/12÷(−1/4)
Answer:
negative
Step-by-step explanation:
the answer will be negative because one fraction is negative and the other is positive. there is nothing to cancel out the negative sign
Compare the graphs of the inverse variations. y=1/x and y=2.5/x
Answer:
The graph of
[tex]y = \frac{2.5}{x} [/tex]
us a vertical stretch of the graph of
[tex]y = \frac{1}{x} [/tex]
by a factor of 2.5.
Step-by-step explanation:
The given functions are
[tex]y = \frac{1}{x} [/tex]
and
[tex]y = \frac{2.5}{x} [/tex]
The graph of
[tex]y = \frac{1}{x} [/tex]
is the parent rational function.
The graph of
[tex]y = \frac{2.5}{x} [/tex]
is a vertical stretch of the parent rational function by a factor of 2.5
how to express quantities as a simplified fraction $45 out of $100
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
Step 1: Simplify
[tex]\frac{45}{100}[/tex]
[tex]\frac{45 / 5}{100/5}[/tex]
[tex]\frac{9}{20}[/tex]
Answer: [tex]\frac{9}{20}[/tex]
Answer:
[tex]\frac{9}{20}[/tex]
Step-by-step explanation:
fraction $45 out of $100means 45/100
the common factors that go into both 45 and 100 is 5
hence divide 45 and 100 by 5
[tex]\frac{45/5}{100/5}[/tex]
= [tex]\frac{9}{20}[/tex]
Expand.
Your answer should be a polynomial in standard form.
(x - 2)(x+2) =
Answer:
[tex]\large\boxed{x^2-4}[/tex]
Step-by-step explanation:
Here we have a Difference of Two Squares:
[tex](a-b)(a+b)=a^2-b^2[/tex]
[tex]\therefore (x - 2)(x+2)=x^2-4[/tex]
Once the standard form of a polynomial is when terms are ordered from the biggest exponent to the lowest exponent,
The polynomial in standard form is [tex]x^2-4[/tex]
Solve the equation:
x^3 + x^2 – 20x=0
Answer: x=0
Step-by-step explanation:
What are the real solutions of the equation x^4= 81?
what is the slope of y= 4.5x
Slope is 4.5 or 9/2
Step-by-step explanation:
Step 1: Compare the equation with the slope intercept form equation y = mx + b where m is the slope and b is the y-intercept.y = 4.5 x
∴ Slope, m = 4.5 or 9/2
what fraction of a clock is represented of the hands are at 12 and 3 asking for my cousin
Answer:
If the hands are at 12 and 3 you would have 1/3
Step-by-step explanation:
At 12 and 3 the hand will take up a third of the clock because at 12 and 3 the clock hands will have a portion of the clock taken up
The fraction of the clock represented when the hands are at 12 and 3 is 1/4.
What is Fraction?A fraction is a mathematical term that represents a part of a whole. It is written in the form of a numerator over a denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the total number of equal parts that make up the whole.
If the hands of a clock are at 12 and 3, then the hour hand is pointing directly at the 3, while the minute hand is pointing directly at the 12.
The fraction of the clock represented by this configuration is the fraction of the total circumference of the clock that is between the 12 and the 3.
Since there are 12 hour markings on a clock face, each hour marking represents 1/12 of the total circumference. Therefore, the distance between the 12 and the 3 is 3/12 or 1/4 of the total circumference.
So, the fraction of the clock represented when the hands are at 12 and 3 is 1/4.
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Josh decided to rent an SUV for a family trip he was planning. On the way
back from his trip, Josh rear-ended another vehicle. Unless he purchased
Josh will have to pay for damages to both vehicles out of his own
pocket.
A. uninsured motorist coverage
B. no-fault accident insurance
c. a collision damage waiver
D. relital-equipment insurance
a collision damage waiver
Josh have to use Collison Damage waiver.
What is Insurance?Managing your risk is possible with insurance. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.
Collision damage waiver (CDW), often known as car rental insurance, releases a car renter from responsibility for all or some accident-related damage to a rental car.
If you are struck by a driver without auto insurance, you are protected by uninsured motorist coverage.
No fault insurance can assist in paying your medical costs and lost wages in the event of a covered accident, regardless of who was at fault.
So, Josh have to use Collison Damage waiver.
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At a store 30 pieces of candy cost a total of $2.40 each piece of candy cost the same amount what is the total cost of 4 pieces of candy
Answer:
0.32
Step-by-step explanation:
First you divide 2.40 by 30 and then it gives you the cost of each individual piece of candy.then you multiply 4 by that amount.
Help!!ASAP ..
Factor completely.
Y^3+6y+8
Answer: The expression is prime and can't be factored with rational numbers.
Step-by-step explanation:
Answer:
I think you meant y^2 + 6y + 8
that is (y + 4)(y + 2)
Step-by-step explanation:
y^3 + 6y + 8 stays the same and cannot be factored
Find the interest. All rates are annual interest rates. Principal $1,000. Rate 8.5 percent Time 3 year
Answer:
interest is $255
Step-by-step explanation:
Answer:$255
Step-by-step explanation:
Principal(p)=$1000
Rate(r)=8.5%
Time(t)=3years
Simple interest(SI)=?
SI=(pxrxt)/100
SI=(1000x8.5x3)/100
SI=25500/100
SI=$255
Bonnie ran 1/4 mile, Olga ran 3/4 mile, Gracie ran
5/4 miles, and Maria ran 2/4 mile. How much
farther, f, did Gracie run than Bonnie and
Maria combined, c?
Answer:
2/4
Step-by-step explanation:
Bonnie and Maria combined = 1/4 + 2/4 = 3/4
Gracie run = 5/4
=> How much farther, f, did Gracie run than Bonnie and Maria combined
= 5/4 - 3/4 = 2/4
So Gracie run 2/4 more than Bonnie and Maria combined
Answer:
2/4 mile.
Step-by-step explanation:
Given:
Db = 1/4 mile
Do = 3/4 mile
Dg = 5/4 mile
Dm = 2/4 mile
Dt = Db + Dm
= 1/4 + 2/4
= 3/4 mile
= Dg - Dt
= 5/4 - 3/4
= 2/4 mile.
Half of a number q is 14 written as a equation
Answer:
q/2=14
Step-by-step explanation:
Half of q is q/2
We know that it is 14
So, q/2=14
7m plus 8 equals 71
How do u solve
Answer: [tex]m=9[/tex]
Step-by-step explanation:
Step 1: Subtract 8 from both sides: [tex]7m+8-8=71-8[/tex]
[tex]7m=63[/tex]
Step 2: Divide both sides by 7: [tex]7m/7=63/7[/tex]
Get your answer: [tex]m=9[/tex]
What does X equal? WILL GIVE BRAINLIEST!
Answer:it is 18
Step-by-step explanation:
You do 40=2x+4 then do 40-4 and get 36 then 36/2 is 18
Topic 6: Kites (Gina Wilson, Geometry)
!!!Please help it’s due Wednesday!!!
All four questions please.
Answer:
35.
So that we have:
KLN = 54 JKN =36
LKN = 72 NMJ = 18
KNM = 126 JLM = 72
LJM = 90 KLM = 126
36.
CE = 6√13
37.
m∠Z = 88°
38.
m∠GFE = 85
Step-by-step explanation:
35.
As KLMN is a kite:
+) KL = KN
=> Triangle KLN is an isosceles triangle.
=> m∠KLN = m∠ KNL = m∠KNJ = 54°
In triangle KLN, total measure of three internal angles are 180 degree, so that: m∠KLN + m∠ KNL + m∠ LKN = 180°
=> 54 + 54 + m∠ LKN = 180°
=> m∠ LKN = 180 - 54 - 54 = 72°
+) KM is the bisector of both Angle LKN and Angle LMN
So that we have:
m∠JKN = 1/2 m∠LKN = 1/2 * 72 = 36°m∠NMJ = 1/2 m∠LMN = 1/2 * 36 = 18°+) KM and LN is perpendicular to each other at point J
=> m∠LJM = 90°
+) m∠KLM = m∠KNM; m∠KLM + m∠KNM + m∠LKN + m∠LMN = 360°
=> m∠KLM + m∠KLM + 72 + 36 = 360
=> 2 m∠KLM = 360 - 72 - 36 = 252
=> m∠KLM = 252/2 = 126 = m∠KNM
+) We have: m∠KLM = m∠KLN + m∠JLM
=> m∠JLM = m∠KLM - m∠KLN = 126 - 54 = 72
36.
As BCDE is a kite, we have:
+) BC = BE; CD = DE = 21
+) BD is perpendicular to CE and intersect each other point F
=> Angle CFD = 90
=> Triangle CFD is the right triangle
According to Pythagoras theorem: CF^2 + DF^2 = CD^2
=> CF^2 = CD^2 - DF^2 = 21^2 - 18^2 = 441 - 324 = 117
=> CF = [tex]\sqrt{117} =3\sqrt{13}[/tex]
+) According to the feature of a kite shape, F is midpoint of CE
=> CF = FE = 1/2 x CE
=>CE = 2 x CF = 2 x [tex]3\sqrt{3} = 6 \sqrt{13}[/tex]
So that CE = 6√13
37.
As given, WXYZ is a kite shape.
According to the feature of a kite shape, angle ZWX and angle ZYX are equal to each other.
=> ∠ZWX = ∠ZYX
=> 8x -23 = 6x +11
=> 8x - 6x = 11 + 23
=> 2x = 34
=> x = 34/2 = 17
=> ∠ZWX = 8x - 23 = 8*17 - 23 = 113°
=> ∠ZWX = ∠ZYX = 113°
As WXYZ is a kite shape, so that total measure of 4 internal angles of it are 360 degree
So that we have:
∠Z + ∠ZWX + ∠ZYX + ∠WXY = 360
=> ∠Z + 113 + 113 + 46 = 360
=> ∠Z = 360 -113 -113-46 = 88°
So that the measure of ∠Z is 88°
38.
As GDEF is a kite shape. As we can see, GE is the longer diagonal, so that it is the bisector of both Angle DGF and Angle DEF.
H is on GE and GE is the bisector of Angle DEF, so we have:
m∠HEF = m∠GEF = 1/2. m∠DEF = 1/2 . (12x- 16)= 6x - 8
As GDEF is a kite shape so that the two diagonals DF and GE are perpendicular to each other, so that: m∠EHF = 90
In the triangle EHF, m∠EHF = 90
=> EHF is a right triangle
=> m∠HEF + m∠EFH = 90
=> 6x - 8 + 3x -1 = 90
=> 9x = 90 + 8 + 1 = 99
=> x = 99/9 =11
=> m∠HEF = 6x - 8 = 6*11 - 8 = 58 = m∠GEF
GE is the bisector of both Angle DGF
=> m∠EGF = 1/2. m∠DGF = 1/2 . 74 = 37
In the triangle GEF, total measure of three internal angles are 180
=> m∠GFE + m∠EGF + m∠GEF = 180
=> m∠GFE + 37 + 58 = 180
=> m∠GFE = 85
Four horses ran in a race
Bart finished third
Dee finished ahead of Bart and caper
Air finished ahead of caper
Air finished behind dee
Which horse won the race?
Answer:
Dee won
Step-by-step explanation:
Using < to mean "finished ahead of ", we are given ...
B = 3
D < B
D < C
A < C
D < A
Dee finished ahead of Air, Bart, and Caper, so Dee won the race.
_____
The order of finish must be D, A, B, C.
what is the ratio of the number of cavities to the volume of soda consumed could be represented by cavities/cm?
Answer:
If the ratio is cavities to volume, you need cavities/V where V is some sort of volume. cm^3 is a volume.
Step-by-step explanation:
one half times (four plus eight)
Answer:
18
Step-by-step explanation:
one half times (four plus eight)
Writing mathematically
1½ ( 4+8)
Using BODMAS
we'll take the bracket first
1½ × 12
Change 1½ to improper fraction = 3/2
3/2 × 12 = 3×6
= 18
I hope this was helpful, please mark as brainliest
Answer: 6.
Step-by-step explanation: First, answer the question in the brackets, that equals 12. Take the 12 and multiply it by 1/2. When you do this, you are basically dividing it by 2, which gives you 6.
Hope this helps!
What would be the answer of my fractions
9 1/2 + 4 3/5=
Answer:
14[tex]\frac{1}{10}[/tex] or [tex]\frac{141}{10}[/tex]
Step-by-step explanation:
Turn your fractions into improper and make them have the same denominator
[tex]\frac{95}{10}[/tex]+[tex]\frac{46}{10}[/tex]=[tex]\frac{141}{10}[/tex]
Leave it as is or simplify to 14 [tex]\frac{1}{10}[/tex]
Answer:
14 1/10
Step-by-step explanation:
Make it to improper fraction
9 1/2 would be 19/2
and 4 3/5 = 23/5
Then to add u have to make the denominators common:
19/2 + 23/5
Both goes common denominator with 20
To make it 20:
(19 × 10/2 ×10) + (23 ×4/5×4)
190 / 20 + 92 / 20
Add those (190 + 92) / 20
282 / 20
Make it to the simplest form:
141 / 10
Then make it mixed fraction:
14 1/10