Answer: 5 and 6
Step-by-step explanation:
X^2 - 11 = (X-1)^2
X^2 - 11 = X^2-2X+1
X^2 - X^2 + 2X = 11+1
2X = 12
X = 6
The preceding number is 5
(6)(6)=36 and (5)(5)=25
36-25=11
The number required is 6
Let the number required bee xIf the number is multiplied by itself, it becomes x²
If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:
x² - 11 = (x - 1)²
x² - 11 = x² - 2x + 1
2x = 11 + 1
2x = 12
x = 6
Hence the number required is 6
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Gail paid a total of $12,000 for stock that was $6 per share. If she sold all her shares for $18,000, how much profit on each share did she make?
A
$9
B
$3
С.
S2000
D
$6.000
Answer:
$3
Step-by-step explanation:
Given
Total Cost Price: $12,000
Unit Cost Price= $6
Total Selling Price = $18,000
Required
Determine the profit on each share
First, we need to determine the units of share bought;
Units = Total cost price / Unit Cost Price
[tex]Units = \frac{\$12000}{\$6}[/tex]
[tex]Units = 2000[/tex]
Next is to determine the selling price of each share; This is calculated as follows;
Unit Selling Price = Total Selling Price / Units Sold
[tex]Unit\ Selling\ Price = \frac{\$18000}{\$2000}[/tex]
[tex]Unit\ Selling\ Price = \$9[/tex]
The profit is the difference between the unit cost price and unit selling price
[tex]Profit = Unit\ Selling\ Price - Unit\ Cost\ Price[/tex]
[tex]Profit = \$9 - \$6[/tex]
[tex]Profit = \$3[/tex]
Hãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)
It looks like we're given the Laplace transform of f(t),
[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]
Start by splitting up F(p) into partial fractions:
[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]
[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]
Complete the square in the denominator,
[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]
and rewrite the numerator in terms of p + 1,
[tex]3p+6 = 3(p+1) + 3[/tex]
Then splitting up the second term gives
[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]
Now take the inverse transform:
[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]
Alex wants to sew a pillow in the shape below. How many square yards of fabric are needed to sew the pillow? Fabric is only sold in increments of ¼ yard.
The shape is missing, so i have attached it.
Answer:
2.6
Step-by-step explanation:
From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.
Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.
Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;
0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,
P0 = πd/2 = π × 0.9/2 =0.45π yds
The perimeter of the inner semicircle would be given as;
PI = πd/2 = π × 0.5/2 =0.25π yds.
Thus, we can calculate the total perimeter of the pillow as;
PT = P0 + PI + 0.2 + 0.2
PT = 0.45π + 0.25π + 0.2 + 0.2
PT ≈ 2.6 yards
Alex will need 2.6 yds
Answer:
0.5
Step-by-step explanation:
Which polynomial can be factored using the binomial theorem?
64x2 + 200x + 625
64x2 + 400x + 625
14,641x4 - 11,979x3 + 9,801x2 – 8,019x + 6,561
14,641x4 - 23,958x3 + 19,602x2 – 16,038x + 6,561
Answer:
B
Step-by-step explanation:
64x2 + 400x + 625=(8x+25)^2
(-t^3+5t^2-6t)+(8t^2-8t)
Answer:
-t^3+13t^2-14t
Step-by-step explanation:
(-t^3+5t^2-6t)+(8t^2-8t)
Combine like terms
-t^3+5t^2+8t^2-6t-8t
-t^3+13t^2-14t
How many skirt-blouse outfits can a woman choose from if she has 5 skirts and 6 blouses?
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
The final price of the textbook for an English literature course is 13.5% more than the listed price when tax and shipping costs are included. If the listed price is $147, what is the final price of the textbook?
(Round to the nearest dollar.)
Answer:
The final price of the textbook rounded to the nearest dollar is $167
Step-by-step explanation:
To solve this problem, we need to find out what 13.5% of $147 equals.
13.5% = 0.135
0.135 x $147 = $19.845
$147 + 19.845 = 166.845
Round to the nearest dollar to get $167
What is the scale factor of the dilation?
A. 2/5
B. 2/3
C. 3/2
D. 8/5
A data set lists earthquake depths. The summary statistics are
nequals=400400,
x overbarxequals=6.866.86
km,
sequals=4.374.37
km. Use a
0.010.01
significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to
6.006.00.
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
What are the null and alternative hypotheses?
A.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμnot equals≠5.005.00
km
B.
Upper H 0H0:
muμnot equals≠5.005.00
km
Upper H 1H1:
muμequals=5.005.00
km
C.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμgreater than>5.005.00
km
D.
Upper H 0H0:
muμequals=5.005.00
km
Upper H 1H1:
muμless than<5.005.00
km
Determine the test statistic.
(Round to two decimal places as needed.)
Determine the P-value.
(Round to three decimal places as needed.)
State the final conclusion that addresses the original claim.
Fail to reject
Upper H 0H0.
There is
evidence to conclude that the original claim that the mean of the population of earthquake depths is
5.005.00
km
Answer:
Step-by-step explanation:
The summary of the given statistics data include:
sample size n = 400
sample mean [tex]\overline x[/tex] = 6.86
standard deviation = 4.37
Level of significance ∝ = 0.01
Population Mean [tex]\mu[/tex] = 6.00
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
To start with the hypothesis;
The null and the alternative hypothesis can be computed as :
[tex]H_o: \mu = 6.00 \\ \\ H_1 : \mu \neq 6.00[/tex]
The test statistics for this two tailed test can be computed as:
[tex]z= \dfrac{\overline x - \mu}{\dfrac{\sigma}{\sqrt {n}}}[/tex]
[tex]z= \dfrac{6.86 - 6.00}{\dfrac{4.37}{\sqrt {400}}}[/tex]
[tex]z= \dfrac{0.86}{\dfrac{4.37}{20}}[/tex]
z = 3.936
degree of freedom = n - 1
degree of freedom = 400 - 1
degree of freedom = 399
At the level of significance ∝ = 0.01
P -value = 2 × (z < 3.936) since it is a two tailed test
P -value = 2 × ( 1 - P(z ≤ 3.936)
P -value = 2 × ( 1 -0.9999)
P -value = 2 × ( 0.0001)
P -value = 0.0002
Since the P-value is less than level of significance , we reject [tex]H_o[/tex] at level of significance 0.01
Conclusion: There is sufficient evidence to conclude that the original claim that the mean of the population of earthquake depths is 5.00 km.
PLSSSS HELPPP MEEEEEE
Hi, I'm happy to help!
Parallel means that two lines are lined up in the same directions and will never intersect even if they were extended forever in directions.
Let's look at the first option of AB, and AD. We can see that both lines intersect at point A, so AB and AD are not parallel.
For the next option of CD and BE, we can see that both lines don't intersect and won't ever even if the lines were extended. So, CD and BE are parallel.
For the third option, we have BC and DE. These lines don't intersect and aren't in line to ever do so. Therefore, BC and DE and parallel.
The last option is AD and BC. These two lines will never meet, but, they aren't line up in the same directions. AD is traveling upwards while BC isn't. Think about being able to make a road out of the two lines, it would never work. AD and BC are not parallel.
To sum it up: You should select the 2nd and 3rd options because those lines are parallel.
I hope this was helpful, keep learning! :D
Write the ratio 4 L : 5.6 L as a fraction in the simplest form with whole numbers in the numerator and denominator
Answer:
Step-by-step explanation:
It's 5/7
You get that by having a calculator that does that. If you don't then the way to do it is multiply the numerator and denominator by 1.25
4 * 1.25 = 5
5.6 * 1.25 = 7
If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?
Answer:
[tex]\huge\boxed{a=9 ; b = -8}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{ax+b}{x}[/tex]
Putting x = 1
=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]
Given that f(1) = 1
=> [tex]1 = a + b[/tex]
=> [tex]a+b = 1[/tex] -------------------(1)
Now,
Putting x = 2
=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]
Given that f(2) = 5
=> [tex]5 = \frac{2a+b}{2}[/tex]
=> [tex]2a+b = 5*2[/tex]
=> [tex]2a+b = 10[/tex] ----------------(2)
Subtracting (2) from (1)
[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]
For b , Put a = 9 in equation (1)
[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]
Which of the following equations is of a parabola with a vertex at (1, 2)?
O y = (x - 1) 2 - 2
Oy= (x - 1)2 + 2
O y = (x + 1)2 - 2
O y = (x + 1)2 + 2
Answer:
the second option: (x-1)squared +2
Explanation:
The x value of the vertex can be found in the parenthesis after the x. However, you have to do the opposite value of it. So, since the paranthesis has (x-1) then that means that the vertex's x-value has to be 1.
For the y-value of the vertex, that can be found after the paranthesis. This value will not be used as the opposite like with the x-value. So, we know that in (x-1)^2 +2 the "+2" indicates the y-value to be 2.
93/28=15/4n-5+4 4/7 i NEED this answer
Answer:
n=1
Step-by-step explanation:
93/28=15/4n-5+4 4/7
93/28=15/4n-5+32/7
93/28=15/4n-35+32/7
93/28=15/4n-3/7
93/28+3/7=15/4n
15/4n=93*7+28*3/28*7
15/4n= 651+84/196
15/4n=735/196
15/4n*4/15=753/196*4/15
n=49/49
n=1
Which of the following expressions are equivalent to (x+y) - (-z)? A. (x+y) - z B. x+ (y+z) C. None of the above
=========================================
Explanation:
Subtracting a negative is the same as adding. Example: 2-(-3) = 2+3 = 5.
So (x+y)-(-z) is the same as x+y+z. We can group up terms inside parenthesis and it won't change the result. Meaning that x+y+z is the same as any of the following below
(x+y)+zx+(y+z)We could also swap the order of either x, y or z, and still have the same result.
look at the image for the question
Answer:
117.8
Step-by-step explanation:
surface area = πr²+πrl, where r = radius and l = slant height
so,
πr²+πrl
= π×3²+π×3×9.5
= 75π/2
= 117.8 (rounded to the nearest tenth)
How many two-digit numbers are there which are multiples of both 2 and 7?
2 digits number = 10-99
Lets find the multiples of 2 and 7 both
Which are = 14, 28,42,56,70,84,98
Therefore there are 7 two digit multiples of both 2 and 7
Must click thanks and mark brainliest
9514 1404 393
Answer:
7
Step-by-step explanation:
Those numbers are 14, 28, 42, 56, 70, 84, 98. There are 7 numbers that are multiples of 2 and 7 (multiples of 14).
(4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000 (c) x 3 100 − 1000x 2 (d) x log x (2) (2 points) U
Answer:
(a) O(x²)
(b) O(x²)
(c) O(x²)
(d) Not O(x²)
Step-by-step explanation:
If a function is O(x²), then the highest power of x in the function ia greater or equal to 2.
(a) 100x + 1000
This is O(x), not O(x²)
(b) 100x² + 1000
This is O(x²)
(c) x³.100 − 1000x²
This is O(x²)
(d) x log x²
This is not O(x²)
The perimeter of a picture frame is
24 inches. If the width of the picture
frame is 5 inches, what is the length of
the picture frame?
Answer:
7 in
Step-by-step explanation:
perimeter = 2length + 2width
Input the given info:
24 = 2length + 2(5)
24 = 2L + 10
14 = 2L
14/2 = L
l = 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find the 84th term of an arithmetic sequence if the first term and common
difference are given as:
ai = 3; d = -4
ag4 =
I
Next
Previous
Answer:
-329
Step-by-step explanation:
1st term a1 = 3, common difference d = -4
84th term,
3+(84-1)(-4)
= -329
Foram prescritos 500mg de dipirona para uma criança com febre.Na unidade tem disponivel ampola de 1g/2ml.Quantos g vão ser administrados no paciente
De acordo com a disponibilidade da unidade, há apenas a seguinte dosagem: 1g/2mL - ou seja, uma grama de dipirona a cada 2mL
O enunciado está meio mal formulado, pois é dito que foram prescritos 500mg de dipirona e é essa quantidade de farmaco que a criança tem que tomar. Deseja-se saber quantos mL deverao ser administrados.
Fazendo a classica regra de 3, podemos chegar no volume desejado:
(atentar que 500mg = 0,5g)
g mL
1 --------- 2
0,5 --------- X
1 . X = 0,5 . 2
X = 1mL(4.8 × 10⁷) + 6,500,000
Answer:
5.45 * 10^7
Step-by-step explanation:
[tex](4.8 * 10^7) +6,500,000[/tex]
= [tex](4.8 * 10^7) + 6.5 * 10^6[/tex]
= [tex](4.8 * 10^7) + (0.65 * 10^7)[/tex]
= [tex]5.45 * 10 ^7[/tex]
How many g of amino acids are in a 2,000mL total parenteral nutrition of 4.25% travesol (amino acids and 20%dextrose?
Answer:
The mass of amino acid present is 85 g
Step-by-step explanation:
From the question we are told that
The volume of the total parenteral nutrition is [tex]V = 2000 mL[/tex]
Generally the volume of the amino acid present is
[tex]V_a = 0.0425 * 2000[/tex]
[tex]V_a = 85 mL[/tex]
Generally
[tex]mass \ \ \alpha \ \ volume[/tex]
So the mass of amino acid present is 85g
f(x) = 2x3 + 7x2 – 4x – 5
g(x) = 3x – 2
Find (f - g)(x).
A. (f - g)(x) = 2x3 + 7x2 – 2 – 3
O B. (f – g)(x) = 2x3 + 7x2 – 2 – 7
O C. (f - g)(x) = 2x3 + 7m2 – 72 – 3
O D. (f - g)(x) = 2x3 + 7x2 – 73 – 7
Answer:
A. 6
B. 2
C. 8
D. 3
all the answers to the previous questions
D.) = 3
The value of the function (f -g)(x) will be 2x^3 + 7x^2 - 7x - 3
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable, Linear function is a function whose graph is a straight line
We are given that the function as;
[tex]f(x) = 2x^3 + 7x^2 - 4x - 5[/tex]
[tex]g(x) = 3x - 2[/tex]
We need to find the function as (f - g)(x)
(f -g)(x) = f(x) -g(x)
(f -g)(x) = 2x^3 + 7x^2 - 4x - 5 - 3x + 2
(f -g)(x) = 2x^3 + 7x^2 - 7x - 3
Therefore, the correct option is C 2x^3 + 7x^2 - 7x - 3
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Use the set of ordered pairs to determine whether the relation is a one-to-one function. {(−6,21),(−23,21),(−12,9),(−24,−10),(−2,22),(−22,−22)}
Answer:
the relation is not one-to-one.
Step-by-step explanation:
it can't because every number is in the 4th quadrant.
Find the distance between the pair of points.
(-6/11, -3)
and (-6/11, 2/3)
The distance between the pair of points is
Type an integer or a simplified fraction.)
Answer:
3 2/3
Step-by-step explanation:
The x value is the same for both points. So we're only trying to figure out the difference in the y values. One y value is three steps down from zero and one y value is 2/3 of a step up from zero. So the total vertical distance between the two points is 3 and 2/3.
What triangle is this
HOPE SO IT HELPS YOU
Answer:
Isosceles.
Step-by-step explanation:
It's an isosceles triangle because 2 sides are congruent ( 2 are 23 yds long).
HELP SOMEONE FOR 20 POINTS
According to a survey, typical American spends 154.8 minutes per day watching TV. A survey of 50 Internet users results in a mean time watching TV per day of 128.7 minutes, with a standard deviation of 46.5 minutes. Which appropriate test we should use to determine if Internet users spend less time watching TV
Answer:
Z > ± 1.645
z= 3.968
Step-by-step explanation:
We formulate the null and alternate hypotheses as
H0 =μ2 ≥ μ1 Ha: μ2 <μ1 one sided
Let α= 0.05
Since the sample sizes are large therefore the test statistic used under H0 is
The critical region for α= 0.05 for a one tailed test Z > ± 1.645
Z = (x`2- x`1) /s/ √n
Z= 154.8-128.746.5/√50
z= 26.1/6.577
z= 3.968
Since the calculated value of z lies in the critical region we reject H0 that internet users spend more time or equal time.