Answer:
Ally
Step-by-step explanation:
The fastest time of the race will be the one lesser in value.
=============================================================
Comparing the tenths place :
⇒ Jill = 8 in the tenths place
⇒ Ally = 8 in the tenths place
⇒ Maria = 9 in the tenths place
Since Maria's time's tenth place value is greater than that of the other two, she had the slowest time.
===========================================================
Comparing the hundredths place (for Jill and Ally) :
⇒ Jill = 7 in the hundredths place
⇒ Ally = 2 in the hundredths place
Since Ally has the lower hundredths' place value, she has the fastest time.
The average Wealth of a person in Richville is $150,000 and the average wealth of a
person in Poorville 15 $20,000. Suppose Richville and Poorville combine to form Mediumville.
Help!!!!! Meeee!! Asappppp
Reason:
Refer to the diagram below. The tiny square angle markers tell us we have a 90 degree angle, meaning those lines are perpendicular.
You can think of the parallel lines being the metal part of train tracks, while the perpendicular line connecting the metal rails is the wooden part of the train tracks.
A class of 30 students plans to collect at least $500 in donations for a rehabilitation camp. They have collected $270. How much more should each student collect?
please please help me I'll give whaever
answer:
1769.344983 or 1769.34 (depends on what you’re rounding to)
explanation:
- the equation for a cylinder‘s surface area is: (2 π r h)+(2 π r^2)
so 2 just means x2
π is just pi
r is your radius and for this equation your radius is 8 cm
and h is your height so for this equation your height is 27.2 cm
- so the equation filled in is:
(2 x π x 8 x 27.2) + (2 x π8^2) = 1769.344983 or 1769.34
(2 x π x 8 x 27.2) = 1367.221123
(2 x π8^2) = 402.1238597
1367.221123 + 402.1238597 = 1769.344983
hope this helps :)
²-6x +10 is to be written in the form (x-p)² +g. Find the values of p and q.
Answer:
[tex]p = 3\\\\q= 1[/tex]
Step-by-step explanation:
[tex]x^2 -6x +10\\\\=x^2 -2 \cdot 3x +3^2 -3^2 +10\\\\=(x-3)^2 -9+10\\\\=(x-3)^2 +1\\\\\text{By comparing with}~ (x-p)^2 +q, \\\\p = 3\\\\q = 1[/tex]
Find the solution set for |2x-3|=9
Answer:
x = 6, -3
Step-by-step explanation:
. . . . . . . . . . . . . . . . .
Find the greatest common factor of 6m² and 7m².
Answer:
your answer is 4 my friend
Step-by-step explanation:
The grade 10 class is going to bake muffins. The recipe that they are going to use requires the following ingredients: RECIPE ✓2 Egga ✔125ml Cooking oll ✓375ml brown sugar (300g) ✓800ml Milk ✓300g Whole wheat flour ✓ 375ml cake flour (210g) ✓5ml Salt ✓ 5ml Vanilla Essence ✓ 10ml Bicarbonate of soda ✓ 250ml Raisins (150g) 2.1 The volume of 150g of Whole wheat is 250ml. Calculate the volume of the Whole wheat flour in the recipe 2.2 When they are all mixed together, all the above ingredients make up 2 litres of mixture (because some parts dissolve into other parts). 2.2.1 Convert 2 litres into ml 2.2.2 How many muffins can the above recipe make if 60ml is required for each muffin? 2.2.3 Using your answer to question 2.2.2, how many eggs will the girls need to buy to make 500 muffins? 2.3 The students need to make 500 muffins, using muffin trays that hold 6 muffins par tray. They plan to put 4 trays at a time into the ovens. Each oven takes 30 minutes to bake. How long will they take to make 500 muffins if they will be using 4 ovens?
The conversion of 2 liters into millimeters from the information regarding the muffins is 2000ml.
How to convert?From the information, we are told to convert 2 litres into ml. This will be:
= 1000 × 2
= 2000ml
The number of eggs that will be bought to make 500 muffins will be:
= 500 × 2
= 1000 eggs.
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Today only a table is being sold for $364.89. This is 38% of its regular price. What was the price yesterday
Answer:
$960.24
Step-by-step explanation:
Hello!
Let the regular price be x.
38% of x = 0.38x
0.38x = 364.89
Solve for x0.38x = 364.89x = 364.89/0.38x = 960.2368421053 ≈ 960.24The price of the table yesterday was around $960.24.
The shorter leg of a right triangle is 5 inches shorter than the longer leg. The hypotenuse is 5 inches longer than the longer leg. Find the side lengths of the triangle.
Answer:
longer leg: 20 in
shorter leg: 15 in
hypotenuse: 25 in
Formulas:
Pythagorean Theorem
[tex]c^2 = a^2 + b^2[/tex]
c ... hypotenuse
a ... one leg
b ... another leg
Pythagorean theorem is used in right triangles (triangles in which one angle is 90°).
Step-by-step explanation:
longer leg: x
shorter leg: x - 5
hypotenuse: x + 5
To find x (longer leg), let's use Pythagorean theorem.
[tex]c^2 = a^2 + b^2\\(x+5)^2 = x^2 + (x-5)^2\\x^2 + 10x + 25= x^2 + x^2 -10x + 25\\x^2 + 10x = 2x^2 - 10x\\0 = x^2 - 20x[/tex]
Now let's factorize to get solutions for x.
[tex]0 = x(x-20)[/tex]
First solution:
[tex]x = 0[/tex]
Second solution:
[tex]x - 20 = 0\\x = 20[/tex]
Since a side of a triangle has to be a positive number, x is equal to 20.
Now let's just substitute x back to get side lengths. From the question the lengths are in inches.
longer leg: x = 20 in
shorter leg: x - 5 = 20 - 5 = 15 in
hypotenuse: x + 5 = 20 + 5 = 25 in
Which shows one way to determine the factors of Which shows one way to determine the factors of x3 + 4x2 + 5x + 20 by grouping? by grouping?
The factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
How to determine the factors?The expression is given as:
x^3 + 4x^2 +5x + 20
Group the expression into two
(x^3 + 4x^2) + (5x + 20)
Factorize each group
x^2(x + 4) + 5(x + 4)
Factor out x + 4
(x^2 + 5)(x + 4)
Hence, the factored expression of the expression x^3 + 4x^2 +5x + 20 is (x^2 + 5)(x + 4)
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y=-3³ +4
step by step of the rules and formula of this equation
Please help me! Thanks.
Answer: Answer:
The perimeter of the polygon are
PQ = 5
RS = 5
PR = √74 = 8.60
QS = √74 = 8.60
QR = 7
Step-by-step explanation:
To calculate the perimeter of a polygon, polygon is like a coordinate with points, to find the length, we use this formula
d = √(x _2 - x_1)^2 + (y_2 - y_1)^2
Let's start from the first two vertices P ( 0 , 4) and Q(5 , 4)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = 4
PQ = √ ( 5 - 0)^2 + ( 4 - 4)^2
= √ 5^2 + 0^2
= √ 25
= 5
Between R( 5 , -3) and S ( 0 , -3)
x_1 = 5
y_1 = -3
x_2 = 0
y_2 = -3
RS = √ ( 0 - 5)^2 + ( -3 - (-3))^2
= √( -5)^2 + ( -3 + 3)^2
= √ 25 + 0
= √ 25
= 5
Between P( 0 , 4) and R (5 , -3)
x_1 = 0
y_1 = 4
x_2 = 5
y_2 = -3
PR = √( 5 - 0)^2 + ( -3 - 4)^2
= √ 5^2 + (-7)^2
= √ 25 + 49
= √ 74
= 8.60
Between Q ( 5 , 4) and S(0 ,-3)
x_1 = 5
y_1 = 4
x_2 = 0
y_2 = -3
QS = √ ( 0 - 5)^2 + ( -3 - 4)^2
= √ -5^2 + -7^2
= √ 25 + 49
= √ 74
= 8.60
Between Q( 5,4) and R(5 , -3)
x_1 = 5
y_1 = 4
x_2 = 5
y_2 = -3
QR = √ (5 - 5)^2 + ( -3 - 4)^2
= √ 0^2 + (-7)^2
= √ 0 + 49
= √ 49
= 7
Step-by-step explanation:
Homework Due Tomorrow please help me it would be great
Answer:
c
Step-by-step explanation:
work out the average for the data below
HELP!!!!!!!!!!!!!!!!!!!!
Answer:
D is the answer hope
Step-by-step explanation:
hope this helped
Forming quadratic expression.Two consecutive odd numbers are such that their product is 35.find the numbers
Answer:
Numbers are 5 , 7
Step-by-step explanation:
Forming quadratic equation and solving:Let the two consecutive odd numbers be (2x + 1) and (2x + 3)
Their product = 35
(2x + 1)(2x + 3) = 35
Use FOIL method.
2x*2x + 2x*3 + 1*2x + 1*3 = 35
4x² + 6x + 2x + 3 = 35
Combine like terms
4x² + 8x + 3 = 35
4x² + 8x + 3 - 35 = 0
4x² + 8x - 32 = 0
Quadratic equation: 4x² + 8x - 32 = 0Solving:
4x² + 8x - 32 = 0
Divide the entire equation by 2
[tex]\sf \dfrac{4}{2}x^2 +\dfrac{8}{2}x - \dfrac{32}{2}=0[/tex]
2x² + 4x - 16 = 0
Sum = 4
Product = -32
Factors = 8 , (-4)
When we multiply 8*(-4) = -32 and when we add 8 + (-4) = 4.
Rewrite the middle term
2x² + 8x - 4x - 16 = 0
2x(x + 4) - 4(x + 4) = 0
(x + 4) (2x - 4) = 0
2x - 4 = 0 {Ignore x +4 = 0 as it gives negative number}
2x = 4
x = 4/2
x= 2
2x + 1 = 2*2 + 1 = 5
2x + 3 = 2*2 +3 = 7
The numbers are 5 , 7
can you help me with this question
Which of the following rules is the composition of a dilation of scale factor 2, then a translation of three units to the right? a) (2x+3,y) b) (2x+6, 2y) c) (2x +3, 2y) d) (2x+6, y)
Answer:
The answer is C: (2x +3, 2y)
Step-by-step explanation:
When applying the dilation of a scale factor of 2, you have to apply it to both the x and y coordinate, which means you are multiplying the coordinates by 2.
Let's assume the coordinates you start with are (x, y). Apply the dilation of 2.
(x, y) -----> (2x, 2y)
Now you are moving the figure right. When moving right, this only effects the x coordinate since the x axis moves left and right. Moving right indicates you will add the number of units translated to the x coordinate.
Translation 2 units right:
(2x, 2y) -----> (2x +3, 2y)
Can someone help me with this math problem?
see attached photo
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
How to determine the value of trigonometric reasons
In this question we must take into accounts the definitions of the trigonometric reasons sine and secant and the Pythagorean theorem as well.
If sec θ < 0 and csc θ > 0, then sin θ > 0 and cos θ < 0, the angle is in the second quadrant (0.5π < θ < π, x < 0, y > 0) and we have the following expression:
sec θ = r/x
[tex]\frac{r}{x}= -\frac{6\sqrt{11}}{11}[/tex]
Then x = - 11, r = 6√11 and the value of y is:
[tex]y = \sqrt{r^{2}-x^{2}}[/tex]
y = 5√11
By trigonometric expressions we have this formula for sin 2θ:
sin 2θ = 2 · sin θ · cos θ
sin 2θ = 2 · (y/r) · (x/r) = (2 · x · y)/r²
sin 2θ = [2 · (- 11) · (5√11)]/396
sin 2θ = - (5/18) · √11
By applying definitions of trigonometric reasons, Pythagorean theorem and a trigonometric expression, the value of the sin 2θ is equal to - (5/18) · √11.
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1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
This means that 0.3 is a (n)
number. Rational or irrational
0.3 is a Rational Number written in Decimal Form
0.3 is neither an Integer nor a Whole number.
Which of the following is equal to this expression?
(256·64)^1/4
A) 4·[tex]\sqrt[4]{4}[/tex]
B) 8·[tex]\sqrt[4]{4}[/tex]
C) 8·[tex]\sqrt[4]{2}[/tex]
D) 2·[tex]\sqrt[4]{2}[/tex]
Answer:
B) [tex]8\sqrt[4]{4}[/tex]
Step-by-step explanation:
[tex](2^{8} *2^{6} )^\frac{1}{4} = (2^{8+6} )^\frac{1}{4} =(2^{14} )^\frac{1}{4} =2^{\frac{7}{2} }=\sqrt{2^{7} } =2^{3} \sqrt{2} =8\sqrt{2} = 8\sqrt[4]{2^{2} } = 8\sqrt[4]{4}[/tex]
the lenghts of five boxes are shown in the table which line plot shows the data from the table
Answer:
The bottom right line plot.
Step-by-step explanation:
In the table, 9 1/4 shows up twice. This can be represented in the line plot by putting 2 x's over the 9 1/4 point.
Which of the following is an even function?
Of(x) = (x - 1)²
Of(x) = 8x
Of(x)=x²-x
Of(x) = 7
COFFE
Sinte echinat
SUMPARNI
Answer:
Step-by-step explanation:
7) $72.45 -28.98 Rounded estimate
Answer:
$43
Step-by-step explanation:
$72.45 can be rounded down to $72.00
$28.98 can be rounded up to $29.00
$72-$29= $43
Solve for p: -3p + 2 > 5
To solve these types of problems:
⇒ just solve like a regular algebraic equation
⇒ with an inequality sign in the middle
Let's solve:
[tex]-3p + 2 > 5\\-3p > 3[/tex]
whenever there is any division/multiplication⇒ must change the inequality sign to face the other direction
[tex]-3p > 3\\p < -1[/tex]
Answer: p < -1
Hope that helps!
Answer:
p < -1
Step-by-step explanation:
-3p + 2 > 5
subtract 2 from both sides
-3p + 2 - 2 > 5 - 2
-3p > 3
divided both sides by -3 to get p alone
-3p / -3 > 3 / -3 reverse the inequality
p > -1
If £2000 is placed into a bank account that pays 3% compound interest per year
how much will be in the account after 2 years?
Answer:
£ 2121.8
Step-by-step explanation:
The formula to find the compound interest is :
[tex]A=P(1+\frac{R}{100} )^n[/tex]
Here,
A = Amount ⇒ ?
P ⇒ Principal ⇒ £2000
R ⇒ Interest rate ⇒ 3%
n ⇒ Time ⇒ 2 years
Let us find now.
[tex]A=P(1+\frac{R}{100} )^n[/tex]
[tex]A=2000(1+\frac{3}{100} )^2[/tex]
[tex]A=2000(1+0.03 )^2[/tex]
[tex]A=2000(1.03 )^2[/tex]
[tex]A=2000*1.0609[/tex]
[tex]A=2121.8[/tex]
Therefore, there will be £ 2121.8 in the bank account after 2 years.
ZA=C
Round your answer to the nearest hundredth.
C
B
6
8
A
?
Answer:
? = 41.41°
Step-by-step explanation:
The known side length is adjacent to the angle we need to find hence we will use cosine
cosx = adjacent /hypotenuse
cos(?) = 6 / 8
simplify fraction, cos(?) = 3 / 4
? = arccos(3 / 4)
X =
(19) Find the values for X and Y, and then solve for the side lengths.
5. Sabrina put $3,000 into a Money Market (high-yield savings)
account with an interest rate of 2.6% compounded quarterly.
a. Write an equation to model the amount in the account over
time.
b. Assuming no deposits or withdrawals are made, how much
money would be in the account after 15 years? Show your
calculation.
c. How would this problem be different if it was compounded
"continuously" instead? Calculate the amount after 15 years.
d. Name 2 or more other situations (other than a savings
account) where you might encounter compound interest later in
your life.
let me answer the last one first
compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.
hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.
hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.
now let's do the others
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]