The average before training with new trainer is 20 mph.
Let the average speed with old trainer be x. Forming the equation as per given information- Average speed with new trainer = 5% × Average speed with old trainer + Average speed with old trainer
Keep the values in formula to find the average speed with old trainer.
21 = 5/100x + x
Multiplying the equation with 100
2100 = 5x + 100x
Performing addition
105x = 2100
Shifting 105 to Right Hand Side of the equation
x = 2100 ÷ 105
Performing division on Right Hand Side of the equation
x = 20
Thus, average speed with old trainer was 20 mph.
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Lisa has to stay under $200.00 while buying new clothes for spring. She has already spent $125.88 and wants to buy some shirts that each cost $20.80. Which of the following inequalities could be used to solve for x, the number of shirts Lisa can buy with the money she has left?
The correct inequality to solve for x will be;
⇒ $20.03x + $125.99 < $200.00
Where, 'x' is the number of shirts.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Lisa buy new clothes for spring under $200.00
She spent $125.88 for buying some shirts that has each cost $20.80.
Let the number of shirts = x
Then, We can formulate for the given condition is;
The inequality for solution of the value of x is,
⇒ $20.03x + $125.99 < $200.00
Because we can solve for x, which is the number of shirts Lisa can buy with the money she has left.
Therefore,
The correct inequality to solve for x will be;
⇒ $20.03x + $125.99 < $200.00
Where, 'x' is the number of shirts.
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Find the product.
(8)(-11)=
Answer:
-88
Step-by-step explanation:
8 x -11 = 88
graph the linear equation 50 points will mark brainliest
You can see the three points where the result is equal to an integer in the photo below. Good luck!
Airplane tickets to Hawaii cost $500. If my mom pays for 8/4 of my ticket, how much will I have to pay?
Answer: so there for the answer is 498
Step-by-step explanation:
500 - 8\4divide 8 by 4which is 2then 500 - 2 = 498Write the sentence as an equation.
271 decreased by k is 230
Suppose you are given the function t(x) = x^2 + 8x - 20 Explain how you would graph this function, making sure to include the following information: Coordinate(s) of the solutions/rootscoordinate of the y-intercept location of the line of symmetrycoordinate of the vertex whether the graph opens up or down and how you know
t(x) = x² + 8x - 20
Coordinate(s) of the solutions/roots
x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0
roots: x= 2 and x = -10
coordinate of the y-intercept
y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20
y-intercept: y = -20
location of the line of symmetry
x = -4
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4
coordinate of the vertex
(-4, -36)
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)
whether the graph opens up or down and how you know
Opens up
Because the coefficient of x² is positive
A book has 250 pages.how many digits have been used to print page no.s of book
Answer: 642 Digits have been used to print 250 Pages
Step-by-step explanation:
A book has 250 pages
1 - 250 Numbers will be used
Single Digit number - 9 ( 1- 9)
Two Digit Numbers 90 ( 10 - 99)
Three Digit Numbers 151 ( 100 - 250)
Number Of Digits used = 9 * 1 + 90 * 2 + 151 * 3
= 9 + 180 + 453
= 642
642 Digits have been used to print 250 Pages
As a fraction in simplest terms, what would you multiply the first number by to get the second? First number: 62 Second number: 52
We will multiply by 26 / 31 in the first number to get second number for fraction in simplest form.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Given that;
In the fraction,
The first number = 62
The second number = 52
Let the number which can be multiply by the fraction = x
Since, The given condition is,
Multiply the first number by to get the second number.
So, We can formulate;
⇒ 62 × x = 52
Solve for x, as;
⇒ 62 × x = 52
⇒ 62x = 52
Divide by 62, we get;
⇒ x = 52 / 62
Multiply and divide by 2;
⇒ x = 26 / 31
Therefore,
We will multiply by the number 26 / 31 in the first number to get second number for fraction in simplest form.
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I really need help with this question
Which shape has an area of b1 + b2 • h ÷2?
Answer:
Trapezoid
Step-by-step explanation:
The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid)
Question 2(Multiple Choice Worth 5 points)
(03.05 LC)
Which of the following is the equation of the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5?
○ (x-1)²+(y+32²-1
25
49
0 (x+12+(y-32²-1
25
49
O(y-322²(x+12²
49
25
O(y+32 (x-12
49
25
+
1
-1
The equation of the the ellipse with a vertical major axis, center at (1, -3), a = 7, and b = 5 is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Equation of the ellipses:
The Equation of the ellipse with center at (h, k)
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}[/tex]
where,
a = length of semi-major axis
b = length of semi-minor axis
Given,
Here we have the value of center as (1, -3) and the values of a = 7 and b = 5.
Here we need to find the equation of the ellipse.
According to the formula we we have the following values are given,
We know the value of center of ellipses is written as,
(h, k) = (1, -3)
And the values of
a = 7 and b = 5
Therefore, when we apply the values on the formula then we get,
[tex]\frac{(x-1)^2}{7^2}+\frac{(y-(-3))^2}{5^2}[/tex]
When we simplify the term then we get,
[tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex]
Therefore, the equation of the ellipse is [tex]\frac{(x-1)^2}{49}+\frac{(y+3)^2}{25}[/tex].
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24. Anna went bowling. She spent less than or equal to $30, but spent more
than $25. Create a number line that shows all the possible amounts that
Anna may have spent at the bowling alley.
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
What is a number line?In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.
Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.
The inequality is given as,
$25 < x ≤ $30
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
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Can you please help me
EXPLANATION
The area of the figure can be obtained by applying the following relationship:
[tex]Area_{paralle\log ram}=base\cdot height[/tex]Where b=base and height=h
In order to find the height, we need to apply the trigonometric relationship:
[tex]\sin 45=\frac{opposite}{\text{hypotenuse}}=\frac{height}{\text{diagonal}}=\frac{h}{6.4}[/tex]Multiplying both sides by 6.4:
[tex]6.4\cdot\sin 45=h[/tex]Solving the argument:
[tex]6.4\cdot0.65=h[/tex]Switching sides:
[tex]h=4.16\text{ inches}[/tex]Now that we have the height, we can compute the area as follows:
[tex]\text{Area}_{\text{parallelogram}}=12.8in\cdot4.16in=53.24in^2[/tex]The answer is 53.24 squared inches.
5x+25=100
Please solve. I don't want any wrong answers!!
Answer:
x=15
Step-by-step explanation:
5x+25=100
Subtract 25 from both sides.
5x+25−25=100−25
5x=75
Divide both sides by 5.
5x÷5=75÷5
x=15
[tex]5x+25=100\\x=[/tex]
Subtract 25 from both sides:
[tex]5x+25-25=100-25\\5x=75[/tex]
Divide both sides by 5:
[tex]\frac{5x}{5} =\frac{75}{5}[/tex]
[tex]\fbox{x=15}[/tex]
Ali is planning a party. He wants to buy some cakes and some sausage rolls. The cakes are sold in boxes. There are 12 cakes in each box. Each box of cakes costs £2.50. The sausage rolls are sold in packs. There are 8 sausage rolls in each pack. Each pack of sausage rolls costs £1.20. Ali wants to buy more than 60 cakes and more than 60 sausage rolls. He wants to buy exactly the same number of cakes as sausage rolls. What is the least amount of money Ali will have to pay?
The amount Ali will pay is £25.80
Define Multiples
A number that can be divided by another number without a remainder.
Multiples of 8 and 12
8 : 8 , 16, 24, 32, 40, 48, 56, 64, 72
12 : 12, 24, 36, 48, 60, 72
common element is 72
72 cakes cost for 12 cakes in each box = 72/12
= 6 packs
cost of 6 packs = 6 * £2.50 = £15
72 sausage rolls for 8 sausage in each box = 72 / 8
= 9 packs
cost of 9 packs = 9 * £1.20 = £10.80
Total cost will be = £15 + £10.80 = £25.80
Hence, the amount Ali will pay is £25.80
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Ji-yoon has a savings account with $690 in it that earns 7% simple interest per year. How much money, to the nearest penny, will Ji-yoon have in 8 years? Give your answer in dollars.
Let's begin by identifying key information given to us:
Principal (p) = $690
Interest rate (r) = 7% = 0.07 per year
Time (t) = 8 years
The amount of money that Ji-yoon has in 8 years is calculated as shown below:
[tex]\begin{gathered} I=p\times r\times t \\ I=690\times0.07\times8=386.4 \\ I=\text{ \$}386.40 \\ \\ \text{The total amount Ji-yoon has after 8 years is:} \\ Total=\text{\$(}386.40+$690$) \\ Total=\text{\$}1,076.40 \end{gathered}[/tex]a poll is given, showing 45% are in favor of a new building project. if 10 people are chosen at random, what is the probability that exactly 8 of them favor the new building project?
Answer:
The probability that exactly 4 of them favour the new building project is 0.0768
what is Probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Step-by-step explanation:
We would assume a binomial distribution for the number of people that are in favour of a new building project. The formula is expressed as
P(x = r) = nCr × p^r × q^(n - r)
Where
x represents the number of successes.
p represents the probability of success.
q = (1 - r) represents the probability of failure.
n represents the number of trials or samples.
From the information given,
p = 40% = 40/100 = 0.4
q = 1 - p = 1 - 0.4
q = 0.6
n = 5
x = r = 4
Therefore,
P(x = 4) = 5C4 × 0.4^4 × 0.6^(5 - 4)
P(x = 4) = 5 × 0.0256 × 0.6
P(x = 4) = 0.0768
Hence, The probability that exactly 4 of them favour the new building project is 0.0768.
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Hello! im stuck on this math question, hope you can help!
Answer:
x = 30
Step-by-step explanation:
The sum of the interior angles of a triangle is 180
x + 65 + x + 55 = 180 Combine line terms
2x + 120 = 180 Subtract 120 from both sides
2x = 60 Divide both sides by 2
x = 30
How many and of which kind of roots does the equation f(x) = x^4 - 2x³ - 11x² + 12x + 36 have?OA. 4 realB. 2 real; 2 complexOC. 4 real; 2 complexD. 3 realReset Selection
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^4\:-\:2x³\:-\:11x²\:+\:12x\:+\:36[/tex]We solve the polynomial as follows:
[tex]\begin{gathered} x^4-2x^3-11x^2+12x+36=0 \\ \\ \left(x+2\right)\frac{x^4-2x^3-11x^2+12x+36}{x+2} \\ \\ \begin{matrix}\texttt{\:\:\:-2¦\:\:\:\:1\:\:\:-2\:\:-11\:\:\:12\:\:\:36}\\ \texttt{\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:-2\:\:\:\:8\:\:\:\:6\:\:-36}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:1\:\:\:-4\:\:\:-3\:\:\:18\:\:\:\:0}\end{matrix} \\ \\ \frac{x^4-2x^3-11x^2+12x+36}{x+2}=x^3-4x^2-3x+18 \\ \\ \left(x+2\right)\frac{x^3-4x^2-3x+18}{x+2} \\ \\ \begin{matrix}\texttt{\:\:-2¦\:\:\:1\:\:-4\:\:-3\:\:18}\\ \texttt{\:\:\:\:¦\underline{\:\:\:\:\:\:-2\:\:12\:-18}}\\ \texttt{\:\:\:\:\:\:\:\:1\:\:-6\:\:\:9\:\:\:0}\end{matrix} \\ \\ \frac{x^3-4x^2-3x+18}{x+2}=x^2-6x+9 \\ \\ (x+2)(x+2)(x^2-6x+9) \\ \\ (x^2-6x+9)=(x-3)^2 \\ \\ (x+2)^2(x-3)^2=0 \\ \\ x+2=0\rightarrow x=-2 \\ \\ x-3=0\operatorname{\rightarrow}x=3 \end{gathered}[/tex]HELP IMMEDIATELY I WILL GIVE 75 BRAINLIST
Answer:
Step-by-step explanation:
(4x + 50)° = 150°
4x = 150° - 50°
4x = 100°
x = 100° / 4 = 25°
Which expression is equivalent to sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12)?
sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) is equivalent to sin(-pi/2)
Define Trigonometric functions
A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.
We know the formula of sin(A - B) = sinAcosB - cosAsinB
And the given expression is
sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Which is in the form of given formula of sin(A - B)
where, A = π/12 and B = 7π/12
put A and B values in sin(A - B),
sin(π/12 - 7π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-6π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-π/2) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Hence, sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12) is equivalent to sin(-π/2).
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Bobby photographs a bird. If the bird, that measures 3.4 inches in the photo, is actually 3.75 feet tall, approximately how long is its boak if it measures 0.4 inches in the
photo?
We need to know about scaling of measurements to solve the problem. The length of the bird's beak is 5.29 inches.
In the given question we know that the height of the bird in the photo is 3.4 inches and the real height of the bird is 3.75 feet. We know that the length of the beak in the photo is 0.4 inches, we need to find out the real length of the beak. We need to find by how much the measurement of the bird is scaled down to fit in the photo. We need to convert feet to inches first to get the scaling factor, we can then divide the length of the beak given by the scaling factor.
3.75 feet= 3.75x12 =45 inches
scaling factor= 3.4/45=0.0756
real length of beak=0.4/0.0756=5.29 inches
Therefore the length of the beak of the bird is 5.29 inches.
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the 10th and 15 term of an AP are - 5 and - 7 1/2 respectively what is the sum of the first 20 terms ? I really need the answer pls A 60 B -105 C -52 1/2 D -20
Answer:
B
Step-by-step explanation:
before finding the sum we require to find first term and common difference.
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then
a₁ + 9d = - 5 → (1)
a₁ + 14d = - 7.5 → (2)
subtract (1) from (2) term by term to eliminate a₁
0 + 5d = - 2.5
5d = - 2.5 ( divide both sides by 5 )
d = - 0.5
substitute d = - 0.5 into (1) and solve for a₁
a₁ + 9(- 0.5) = - 5
a₁ - 4.5 = - 5 ( add 4.5 to both sides )
a₁ = - 0.5
the sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
here a₁ = - 0.5 and d = - 0.5 , then
S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]
= 10 (- 1 -9.5)
= 10 × - 10.5
= - 105
What is 3 / 5 x 8/9?
A. 8 /15
B. 11 /14
C. 27 / 40
D. 91 /40
Answer:
A) 8/15
Step-by-step explanation:
3 / 5 x 8/9
(3/5)(8/9)
(3*8)/(5*9)
(24/45)
8/15
Answer:
8/15
Step-by-step explanation:
3 / 5 x 8/9
Multiplying fractions
Rewriting
3/9 * 8/5
Simplify
1/3 * 8/5
Multiply the numerators
1*8 =8
Multiply the denominators
3*5 = 15
8/15
Write the linear equation in standard form.
y - 2 = 1/3(x + 6)
Answer: y=x/3 + 4
Step-by-step explanation:
distribute 1/3 to the (x+6): x/3 + 2add two to both sides: y=x/3 + 4
Before a piece of steel can be sold for its maximum price, it must be 35 feet long with an absolute error of 1 foot. Find the range of acceptable heights for steels that are to be sold at full price by writing an absolute value inequality to represent this situation then solving it.
Let's call x to the height. The inequality that represents an acceptable range is:
|x - 35| ≤ 1
Solving it, we get:
x - 35 ≤ 1 or x - 35 ≥ -1
x ≤ 1 + 35 x ≥ -1 + 35
x ≤ 36 x ≥ 34
which is equivalent to 34 ft ≤ x ≤ 36 ft
PLEASE HELP!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
The standard form of the equation of f(x) is option a -x² - 6x + 7
Given,
The graph shows a downward open parabola.
The vertex points are:
(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)
Now,
We have to find the standard form of the function f(x):
As from the graph:
Parabola opens downward, so the function will be negative.
We have the options with:
a = -1, b = -6 and c = 7
Now,
Use x = -b/2a
x = 6/2 × -1 = 6/-2 = -3
Now,
f(x) = -x² - 6x + 7
f(-3) = -(-3)² - 6(-3) + 7
f(-3) = -9 + 18 + 7
f(-3) = 9 + 7
f(-3) = 16
That is, the points for the vertex in this equation is (-3, 16)
Then, the standard form of the equation of f(x) is option a -x² - 6x + 7
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Whats 1+1?
(Just a joke)
Answer:
either 11 or 21
Step-by-step explanation:
tho I might be 2
Determine whether the table of values represents a linear function. If so, write the function.
PLEASE HELP!!
Loren solved the equation 10 = startfraction 19 over 9 endfraction (149) b for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). what error did loren make?
The eqations are 149=19/9 (10) +b and 130=19/9(1)+b
Given that,
As part of her work, Loren found the solution to the equation 10 = start fraction 19 over 9 end fraction (149) b for b and the points are (1, 130) and (10, 149)
Finding the slope of a line that goes through two locations for Loren is as follows: m=y2-y1/x2-x1
=149-130/10-1
=19/9
m=19/9
There are two ways to solve for b in the equation y=mx+b for the location (1,130), where y=130, x=1, and m=19/9, and for the position (10,149), where 149=19/9 (10) +b.
Therefore, the equation of a trend line that passes through the points (1, 130) and (10, 149) are 149=19/9 (10) +b ,130=19/9(1)+b
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