Answer:
12 inches
Step-by-step explanation:
A=1/2bh
30=1/2b5
(30*2)/5=b
B=12
At what rate per annum will N250 amount to N330 in 4 years.
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{8 \: \% \: }}}}}[/tex]Step-by-step explanation:
Given,
Principal ( P ) = N 250
Time ( T ) = 4 years
Amount ( A ) =N 330
Rate ( R ) = ?
First, finding the Interest :
According to definition of Amount ,
Amount = Principal + Interest
plug the values
⇒[tex] \sf{330 = 250 + I}[/tex]
Move i to left hand side and change it's sign
⇒[tex] \sf{ - I = 250 - 330}[/tex]
Calculate
⇒[tex] \sf{ - I = - 80}[/tex]
Change the signs of the both equation
⇒[tex] \sf{I = 80 }[/tex]
Interest = 80
Finding the rate :
Simple Interest = [tex] \sf{ \frac{PTR}{100} }[/tex]
plug the values
⇒[tex] \sf{80 = \frac{250 \times 4 \times R}{100} }[/tex]
Multiply the numbers
⇒[tex] \sf{80 = \: \frac{1000 \: R}{100} }[/tex]
Apply cross product property
⇒[tex] \sf{1000R = 100 \times 80}[/tex]
Multiply the numbers
⇒[tex] \sf{1000R = 8000}[/tex]
Divide both sides of the equation by 1000
⇒[tex] \sf{ \frac{1000R}{1000} = \frac{8000}{1000} }[/tex]
Calculate
⇒[tex] \sf{R = 8 \: \% \: }[/tex]
Thus, Rate = 8 %
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Let's learn about Principal , Interest , Time , Rate and Amount :
Principal = The money which is borrowed or deposited is called principal.Interest = The additional amount of money which is paid by borrower to the lender is called interest.Time = The duration of time for which principal us deposited or borrowed is termed as time period.Rate = The condition under which the insterest is charged is called rate.Amount = The sum of principal and Interest is called an amount.Hope I helped!
Best regards!!
Type the correct answer in the box. Use numerals instead of words. The height of a baseball, in feet, is represented by this expression, where t is time in seconds. -16t squared+64t+3 The height of the baseball after 3.5 seconds is BLANK feet.
Answer:
31 Feets
Step-by-step explanation:
Given the expression for the height of a baseball:
Height(t) = -16t^2 +64t +3
Height in Feets ; time (t) in seconds
Height of baseball after 3.5 seconds :
Height(3.5) = -16(3.5)^2 + 64(3.5) + 3
Height = - 16(12.25) + 64(3.5) + 3
Height = - 196 + 224 + 3
Height = 31 Feets
Height after 3.5 seconds = 31 feets
what is the value of 600.79-40.0032+5.01 to the nearest Hundredths
Answer:
565.80
Step-by-step explanation:
600.79-40.0032+5.01 = 565.7968
565.7968 to the nearest Hundredths =
565.80
Answer:
565.80
Step-by-step explanation:
600.79 - 40.0032 + 5.01
600.79 - 40.0032 = 560.7868
560.7868 + 5.01 = 565.7968
565.7968 to the nearest hundredth = 565.80
Please answer this question now
Answer:
320 sq in
Step-by-step explanation:
4(1/2*8*16) + (8*8)
= 4(64) + (64)
= 5(64)
= 320
Find all the solutions to \[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][tex]Find all the solutions to\[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][/tex]
Answer:
x = -4 + 3 i or x = -4 - 3 i
Step-by-step explanation:
Solve for x:
(x + 4)/(x + 5) = (x - 5)/(2 x)
Hint: | Multiply both sides by a polynomial to clear fractions.
Cross multiply:
2 x (x + 4) = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
2 x^2 + 8 x = (x - 5) (x + 5)
Hint: | Write the quadratic polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
2 x^2 + 8 x = x^2 - 25
Hint: | Move everything to the left hand side.
Subtract x^2 - 25 from both sides:
x^2 + 8 x + 25 = 0
Hint: | Using the quadratic formula, solve for x.
x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:
x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2
Hint: | Express sqrt(-36) in terms of i.
sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):
x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2
Hint: | Simplify radicals.
sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:
x = (-8 + i×6)/2 or x = (-8 - i×6)/2
Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.
Factor 2 from -8 + 6 i giving -8 + 6 i:
x = 1/2-8 + 6 i or x = (-8 - 6 i)/2
Hint: | Cancel common terms in the numerator and denominator.
(-8 + 6 i)/2 = -4 + 3 i:
x = -4 + 3 i or x = (-8 - 6 i)/2
Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.
Factor 2 from -8 - 6 i giving -8 - 6 i:
x = -4 + 3 i or x = 1/2-8 - 6 i
Hint: | Cancel common terms in the numerator and denominator.
(-8 - 6 i)/2 = -4 - 3 i:
Answer: x = -4 + 3 i or x = -4 - 3 i
can someone explain this please?
Answer:
Hey there!
Our equation can be: 2y+3=4y+2
Hope this helps :)
Answer:
2y+3=4y+2
I hope you got it..
Find the degree of the monomial.
s8t
The degree is
Answer:
Step-by-step explanation:
the degree of 8^8t
16777216t : the degree of the mnonmial is 1, because the degree of the variable is 1
How would you write Twice the difference of 9 and a number.
Answer:
Hey there!
You would write that as 2(9-n), where n is the number.
Hope this helps :)
A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15. Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing? (–6, –3) (–3, –1) (–3, 0) (–6, –5)
Answer:
Step-by-step explanation:
The only place that the function is increasing is [-3, -1] (learn your interval notation). At x = -3, y = -11; at x = -2, y = -6 (-6 is greater than -11); and at x = -1, y = -1 (-1 is greater than -6). The next x value, 0, returns a y value of -2. But -2 is less than -1, the value before it, so it begins deceasing again at x = 0.
Based on the values given in the table for f(x), the interval of x-values that show the function increasing is (-3, -1).
Which interval shows the function increasing?The value of f(x) was decreasing from 34 until it got to -11 where it then started to rise again. The relevant value of x here is -3.
The value then began to rise until it reached -1 where it then fell to -2. The x value here is -1.
The interval of x-values where the function is increasing is therefore (-3, -1).
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Roberto is x years older than his only sister but 10 years ago he was twice her age. What are the current ages of the siblings?
Answer:
S = x + 10
R = 2x + 10
Step-by-step explanation:
If R is Roberto's age, and S is his sister's age, then:
R = S + x
R − 10 = 2 (S − 10)
Solve with substitution.
S + x − 10 = 2 (S − 10)
S + x − 10 = 2S − 20
S = x + 10
R = 2x + 10
How many of the positive integer factors of 15552 are perfect squares?
There are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
What is factors?Factors can be define splitting the value in multipliable values.
Factorization of 15552
= 1 * 4 * 4 * 4* 9 * 9 * 3
Perfect squares can be formed by above factors are
= 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
Thus, there are 12 factors which are perfect squares is 1, 4, 9, 16, 36, 64, 81, 144, 324, 576, 1296, 5184.
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) Martha went to the store with $75.00. She bought 3 pairs of socks for $4.00 each, she bought 2 shirts for $20.00 each, and she bought a skirt for $21.00. How much money did she have left?
Answer:
She had $2.00 left.
Step-by-step explanation:
PEMDAS
$75 - [(3 x $4) + (2 x $20) + $21 ]
$75 - [ $12 + $40 + $21]
$75 - [ $52 + $21]
$75 - $73
$2
A line that contains the points (5, −3) and (7, 3) has a slope, m, that equals
Answer:
m = 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (5, - 3) and (x₂, y₂ ) = (7, 3)
m = [tex]\frac{3+3}{7-5}[/tex] = [tex]\frac{6}{2}[/tex] = 3
If f(x) = 3x^2 + 2 and g(x) = x^2- 9, find (f-g)(x).
O A. 4x2 - 7
O B. 2x2 +11
O c. 2x2 - 7
O D. 4x2 +11
Answer:
[tex] \boxed{\sf B. \ 2x^{2} + 11} [/tex]
Given:
f(x) = 3x² + 2
g(x) = x² - 9
To Find:
(f - g)(x)
Step-by-step explanation:
[tex]\sf (f -g)(x) = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} + 2) - (x^{2} - 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} + 2 - x^{2} + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} - x^{2} + 2 + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} - x^{2}) + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + 11 [/tex]
The line plot below displays the fraction of incoming calls answered before the second ring by a group of employees. What fraction of employees answered less than of their incoming calls before the second ring?
Answer:
1/6
Step-by-step explanation:
People who answered less than 1/2 were: 2 + 1 + 3 = 6 people.
There are a total of 36 people.
People who answered their calls before the second ring were only 6/36.
When we simplify the fraction, we get 1/6.
So, the answer is 1/6
Which of the following statements is true according to the measurements in the diagram?
Let's look at the corresponding ratios:
[tex]\frac{AB}{ED}=\frac{24}{30}=\frac{4}{5}\\
\frac{BC}{DC}=\frac{16}{20}=\frac{4}{5}\\
\frac{AC}{EC}=\frac{21}{28}=\frac{3}{4}\\[/tex]
And we see that the three aren't equal.
Hence, $\Delta ABC$ and $\Delta EDC$ are not similar.
Answer:
°[Option 3] => Triangle ABC and Triangle EDC are not similar
Step-by-step explanation:
The angles nor the sides are congruent in this image.
Please mark Brainliest
Make the biggest possible number using the digits below only once 0 , 3 , 4
Answer:
12,157,665,459,057,000,000
Step-by-step explanation:
It seems like it would have to involve exponents. 3 to the 40th power would be 12,157,665,459,057,000,000.
19 x97 find the product using suitable properties
Answer:
19 x 97 = 1843
3/4a-1/6=2/3a+1/4? Please i need help!!!!
Answer: a=5
Step-by-step explanation:
1/12a=10/24
24a=120
a= 5
6
1 point
Label the steps in order to solve the following equation:
-11 - 5z = 6 (5z + 4)
&
1
-11 - 5z = 30z + 24
2
-35 = 352
3
-11 = 352 + 24
4
-1=2
Answer:
swap the middle two steps to put them in order
Step-by-step explanation:
The steps in order would be ...
-11 -5z = 30z +24 . . . . . eliminate parentheses-11 = 35z +24 . . . . . . . . add 5z-35 = 35z . . . . . . . . . . . . subtract 24-1 = z . . . . . . . . . . . . . . . . divide by 2Variance 0.7775
Find the standard deviation (hint: the standard deviation is the square root of the variance)
Answer:
0.88175960442
Step-by-step explanation:
The square root of 0.7775 is 0.88175960442
The value of standard deviation will be;
⇒ 0.8803
What is mean by square root of a number?
A square root of a number is a value that multiplied by itself gives the same number.
Given that;
The value of Variance = 0.7775
Now,
Since, The standard deviation is the square root of the variance.
Hence, We can formulate;
The value of standard deviation = √0.7775
= 0.8803
Thus, The value of standard deviation will be;
⇒ 0.8803
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Please help, 50 points! :) Please do all parts
you WILL get brainiest
PDF attached below
1. The first step here is to arrange the data set's form least to greatest,
Sherelle: 26, 39, 56, 58, 60, 62, 65, 66, 66, 68, 71, 72, 72, 73, 74, 75, 81, 83, 84, 85
Venita: 44, 45, 51, 51, 53, 53, 55, 57, 58, 62, 65, 66, 69, 69, 70, 73, 75, 77, 78, 79
Now we can determine our 5 - number summary based on the numbers respective positions.
First Data Set,
(Five - Number Summary) - Minimum : 26, Quartile 1 : 60, Median : 69.5, Quartile 3 : 75, Maximum : 85
Second Data Set,
(Five - Number Summary) - Minimum : 44, Quartile 1 : 53, Median : 63.5, Quartile 3 : 73, Maximum : 79
2. This part is based on your drawings of the box and whisker plots, so you would have to figure that part out by yourself.
3. First off we know that our data set is composed of the years from 1900, so let's rewrite the set based off of the actual year -
Sherelle: 1926, 1939, 1956, 1958, 1960, 1962, 1965, 1966, 1966, 1968, 1971, 1972, 1972, 1973, 1974, 1975, 1981, 1983, 1984, 1985
Venita: 1944, 1945, 1951, 1951, 1953, 1953, 1955, 1957, 1958, 1962, 1965, 1966, 1969, 1969, 1970, 1973, 1975, 1977, 1978, 1979
( a ) Now in Sherelle's defence, she can say that the lowest coin date in her group is 1926, comparative to Venita's group - the lowest coin date in hers being 1944. Therefore, she is more likely to have the 1916 coin, after all that date is the lowest overall in both their data set.
( b ) In Venita defence, she can say that the mean of her data set is lower than the mean of Sherelle's data set. Take a look at the calculations below,
Sherella's Mean : [tex]\frac{39336}{20}[/tex] = [tex]\frac{9834}{5}[/tex] = 1966.8,
Venita's Mean : [tex]\frac{39250}{20}[/tex] = [tex]\frac{3925}{2}[/tex] = 1962.5
( c ) I would say Sherella's bag would most likely contain the 1916 coin. The mean is a prominent factor, but their mean(s) only differ by a very small quantity. That too, Sherella's bag contains the lowest coin in both their groups, and though that is not a prominent factor, it could be that she does have the 1916 coin.
5/14, 7/10, 5/6, 11/15, 19/2
Answer:
5/14 = 0.36
7/10 = 0.7
5/6 = 0.83
11/15 = 0.73
19/21 = 0.9
(round to the tenth)
so the answer is;
5/14, 7/10, 11/15, 5/6, 19/21
Step-by-step explanation:
Hope it helps!
What is the answer to (6/7)/(12/21) = 4/x Algebra plz help
Answer:
(6/7)/(12/21) = 4/x
the first part of the expression :
when divide fraction: turn the sign from ÷ to × and flip the second fraction
(6/7)×(21/12)=4/x
126/84=4/x ( simplify the fraction 126/84)
GCF of 126 and 84 is 42 ( 126/48=3 and 84/42=2)
3/2=4/x ( cross multiplication ( butterfly)
1.5=4/x
1.5x=4
x=4/1.5=2.6666.......
Melissa put her $500 In a savings account that earns 4% interest compounded annually. How much will be in the account after 3 years? Round your answer to the nearest hundredth
Work Shown:
A = P*(1+r/n)^(nt)
A = 500*(1+0.04/1)^(1*3)
A = 562.432
A = 562.43
Answer: $562.43
Step-by-step explanation:
The initial start up amount is 500 and we want to expressed this as an exponential function. So since we know the initial value we need to find the rate of change. So if you earn 4% interest you are earning 4% percent more on top the actual 100%.
So 100% + 4 % = 104% = 1.04
The common difference is 1.04.
so 500 * 1.04^n= A where n is the number of years and A is the total amount.
A = 500 * [tex]1.04^{3}[/tex]
A= 562.43
A grocery store bought some mangoes at a rate of 5 for a dollar. They were separated into two stacks, one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar. What was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes?
Answer:
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
Step-by-step explanation:
Let the number of mangoes bought by the grocery store be n. Also let the number of mango sold for $3 in one stack be x and the number of mango sold for $6 in the second stack be y.
Therefore:
x + y = z (1)
Also, the mangoes was sold at break even price, that is the cost of the mango and the price it was sold for was the same. Therefore:
Cost of buying = Price it was sold for
The cost of the mango = 5z and the price it was sold for = 3x + 6y
3x + 6y = 5z (2)
Substituting z = x + y in equation 1
3x + 6y = 5(x + y)
3x + 6y = 5x + 5y
6y - 5y = 5x - 3x
y = 2x
x / y = 1/ 2 = 1 : 2
The ratio of the number of mangoes in the $3 stack to those in the $6 stack is 1 : 2
Given: D is the midpoint of AB; E is the midpoint of AC.
Prove: DE BC
y
Complete the missing parts of the paragraph proof.
Proof:
To prove that DE and BC are parallel, we need to show
that they have the same slope.
slope of DE = 12-11=_C-C
X2 - x1 a + b - b
A(2b, 2c)
D(b, c)
Ela + bc)
slope of BC =
B(0,0)
C(2a, 0)
Therefore, because
DE 1 BC.
Answer:
The lines DE and BC have the same slope, therefore the two lines, DE and BC, are parallel
Step-by-step explanation:
To prove that DE is parallel to BC, we have;
The slope, m of the lines DE and BC are found from the following equation;
[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where;
(x₁, y₁) and (x₂, y₂) = (b, c) and (a + b + c) for DE, we have;
[tex]Slope, \, m =\dfrac{c - c}{a + b-b} = 0[/tex]
Where we have (x₁, y₁) and (x₂, y₂) = (0, 0) and (2a, 0) for BC, we have;
[tex]Slope, \, m =\dfrac{0 - 0}{2a-0} = 0[/tex]
Therefore, because the lines DE and BC have the same slope, the two lines DE and BC are parallel.
Answer:
slope of DE = 0
slope Bc = 0
slopes are =
Step-by-step explanation:
If an arrow is shot upward on Mars with a speed of 62 m/s, its height in meters t seconds later is given by y = 62t − 1.86t². (Round your answers to two decimal places.) Estimate the speed when t = 1. Can you please show me the steps to solve this?
Answer:
Approximately [tex]58.28\; \rm m \cdot s^{-1}[/tex].
Step-by-step explanation:
The velocity of an object is the rate at which its position changes. In other words, the velocity of an object is equal to the first derivative of its position, with respect to time.
Note that the arrow here is launched upwards. (Assume that the effect of wind on Mars is negligible.) There would be motion in the horizontal direction. The horizontal position of this arrow will stays the same. On the other hand, the vertical position of this arrow is the same as its height: [tex]y = 62\, t - 1.86\, t^2[/tex].
Apply the power rule to find the first derivative of this [tex]y[/tex] with respect to time [tex]t[/tex].
By the power rule:
the first derivative of [tex]t[/tex] (same as the first derivative of [tex]t^2[/tex] (same as [tex]t[/tex] to the second power) with respect toTherefore:
[tex]\begin{aligned}\frac{dy}{d t} &= \frac{d}{d t}\left[62 \, t - 1.86\, t^2\right] \\ &= 62\,\left(\frac{d}{d t}\left[t\right]\right) - 1.86\, \left(\frac{d}{d t}\left[t^2\right]\right) \\ &= 62 \times 1 - 1.86\times\left(2\, t) = 62 - 3.72\, t\end{aligned}[/tex].
In other words, the (vertical) velocity of this arrow at time [tex]t[/tex] would be [tex](62 - 3.72\, t)[/tex] meters per second.
Evaluate this expression for [tex]t = 1[/tex] to find the (vertical) velocity of this arrow at that moment: [tex]62 - 3.72 \times 1 =58.28[/tex].
Answer:
58.28 m/s
Step-by-step explanation:
y = 62t - 1.86t²
Speed, S = dy/dt = 62 - 2(1.86)t
S = 62 - 3.72t
When t = 1
S = 62 - 3.72 = 58.28 m/s
this is urgent...please help!
the brown family is ordering pizza. they are trying to decide whether to order a large pizza or a monster pizza. a monster pizza (m) has six fewer slices than twice the number of slices on a large pizza (l). the difference between the number of slices on a monster pizza and the number of slices on a large pizza is five slices. which system of equations below can be used to determine the number of slices on a large pizza and a monster pizza?
a) m - 2 l = 5
m - l = 6
b) 2m - l = 6
m - l = 5
c) 2m - l = -6
m - l = 5
d) m - 2 l = - 6
m - l = 5
Answer:
d) m - 2 l = - 6; m - l = 5
Step-by-step explanation:
Twice the number of slices on a large pizza is 2l. 6 fewer than that is 2l-6. This is the number on a monster pizza, so we have ...
m = 2l -6
Subtracting 2l from both sides gives the equation ...
m -2l = -6 . . . . . matches choice D
Work out the circumference of a circle with diameter 1.8 cm.
Take a to be 3.142 and give your answer to 1 decimal place.
Answer:
The answer is
5.6 cmStep-by-step explanation:
Circumference of a circle( C) = πd
where d is the diameter
π = 3.142
From the question
d = 1.8cm
Substitute d = 1.8 into the above formula
Circumference of the circle is
3.142 × 1.8
= 5.6556
We have the final answer as
C = 5.6 cm to one decimal placeHope this helps you
