Answer:
21
Step-by-step explanation:
(-4)(-2)+2(6+5)
(8)+2(11)
10+11
21
Hope this helps! :)
Answer:32
Step-by-step explanation: First, we do parentheses. 6+5 = 11. Next, we have to do multiplication (-4)(-2) is positive 8 because there are two negatives. 8+2 is 10 + 2(11) is 10+22 which is 32
A glass vase weighs 0.17 lb. How much does a similarly shaped vase of the same glass weigh if each dimension is 6 times as large?
Answer:
7,647.4?
Step-by-step explanation:
Calculate the volume of a sphere that has a radius of 4 meters
Answer:
268.08
Step-by-step explanation:
use the formula 4/3πr^3Answer:
803.84 m³
Step-by-step explanation:
The formula to find the volume of a sphere is:
V = 4 π r³
Given that,
radius ⇒ 4m
Let us find the volume now.
V = 4 π r³
V = 4 π × ( 4 )³
V = 4 π × 64
V = 4 π × 64
V = 12.56 × 64
V = 803.84 m³
6. Find the values of x and y. 30° 17
Answer:
X = 17√3
Y = 34
Step-by-step explanation:
TO calculate the values of X and y we use SOHCAHTOA.
Calculating for Xtan 30 = opposite/adjacent
tan30 = 17/X
Cross multiply
tan30 ×X = 17
Divide bothsides by tan30
Note: tan30= 1/√3X = 17/1/√3
X=17√3
X= 29.4X = 29 ( approximately)
Calculating for y[tex]sin30 = \frac{Opposite}{Hypothenus} \\ \\ sin30 = \frac{17}{y} [/tex]
Cross multiply[tex]sin30 \times y = 17[/tex]
Divide bothsides by sin30[tex] \frac{sin30 \times y}{sin30} = \frac{17}{sin30} \\ \\ y = \frac{17}{0.5} = 34 \\ y = 34[/tex]
About 5% of the population has a particular genetic mutation. 300 people are randomly selected.
Find the standard deviation for the number of people with the genetic mutation in such groups of 300. Round your answer to two decimal places.
The standard deviation for the number of people with the genetic mutation is 3.77
How to determine the standard deviation?The given parameters are:
Sample size, n = 300
Proportion that has the particular genetic mutation, p = 5%
The standard deviation for the number of people with the genetic mutation is calculated as:
Standard deviation = √np(1 - p)
Substitute the known values in the above equation
Standard deviation = √300 * 5% * (1 - 5%)
Evaluate the product
Standard deviation = √14.25
Evaluate the exponent
Standard deviation = 3.77
Hence, the standard deviation for the number of people with the genetic mutation is 3.77
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The Red Label Scotch Company is planning to produce 600 litres of Scotch Whisky. Three components A, B & C are mixed to form the final product. Component A, B and C cost Rs.10, Rs.15 and Rs.20 per litre respectively. In the final product, the amount of A component to be 2½ times the amount of component C. The total cost of the components should be Rs.8250. Determine the quantity of each components which should be included in the final product. (Use inverse of matrix Method).
Answer:
c
Step-by-step explanation:
(x^2-y^2)dx+2xydy=0
so this is a problem of a differential equation I've been trying so hard to match with the given answer but failed every time I tried. So, is there anyone who can really can help me out to catch the mistakes that I'm making?
* The last line of my workout is just a dump guess.
The pictures are my workouts also the answer to this question is attached. Please read my solutions by this order : pic-1, pic-3 & pic-2, if necessary.
[tex](x^2 - y^2) \, dx + 2xy \, dy = 0[/tex]
Multiply both sides by [tex]\frac1{x^2}[/tex].
[tex]\left(1 - \dfrac{y^2}{x^2}\right) \, dx + \dfrac{2y}x \, dy = 0[/tex]
Substitute [tex]y=vx[/tex], so [tex]v=\frac yx[/tex] and [tex]dy=x\,dv+v\,dx[/tex].
[tex](1-v^2) \, dx + 2v (x\,dv + v\,dx) = 0[/tex]
[tex](1 + v^2) \, dx + 2xv \, dv = 0[/tex]
Separate the variables.
[tex]2xv\,dv = -(1 + v^2) \, dx[/tex]
[tex]\dfrac{v}{1+v^2}\,dv = -\dfrac{dx}{2x}[/tex]
Integrate both sides
[tex]\displaystyle \int \frac{v}{1+v^2}\,dv = -\frac12 \int \frac{dx}x[/tex]
On the left side, substitute [tex]w=1+v^2[/tex] and [tex]dw=2v\,dv[/tex].
[tex]\displaystyle \frac12 \int \frac{dw}w = -\frac12 \int\frac{dx}x[/tex]
[tex]\displaystyle \ln|w| = -\ln|x| + C[/tex]
Solve for [tex]w[/tex], then [tex]v[/tex], then [tex]y[/tex].
[tex]e^{\ln|w|} = e^{-\ln|x| + C}[/tex]
[tex]w = e^C e^{\ln|x^{-1}|}[/tex]
[tex]w = Cx^{-1}[/tex]
[tex]1 + v^2 = Cx^{-1}[/tex]
[tex]1 + \dfrac{y^2}{x^2} = Cx^{-1}[/tex]
[tex]\implies \boxed{x^2 + y^2 = Cx}[/tex]
Your mistake is in the first image, between third and second lines from the bottom. (It may not be the only one, it's the first one that matters.)
You incorrectly combine the fractions on the left side.
[tex]\dfrac1{-2v} -\dfrac v{-2} = \dfrac1{-2v} - \dfrac{v^2}{-2v} = \dfrac{1-v^2}{-2v} = \dfrac{v^2-1}{2v}[/tex]
If my goal was to be above 85% I my final number was 80 what was my percentage for the month?
Using it's concept, your percentage for the month was of 94.12%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
P = a/b x 100%
In this problem, your goal was of 85, with a grade of 80, hence the percentage is:
P = 80/85 x 100% = 94.12%.
Hence, your percentage for the month was of 94.12%.
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i need help w this pls
Answer: C
Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
Answer:
7.....gggggggggggggggh
△ABC has vertices A(-2, 0), B(0,8), and C(4,2). Find the coordinates of the point of congruency of the altitudes (H)
Based on the calculations, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
What is a triangle?A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Assuming the following parameters for triangle ABC:
Let AM be the altitudes on BC.Let BN be the altitudes on CA.Let CL be the altitudes on AB.For the slope of BC, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2.
For the slope of CA, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3.
For the slope of AB, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4.
Note: The point of concurrency of three altitudes in a triangle is referred to as orthocenter.
Since side AB is perpendicular to side QC, we have:
m₁ × m₂ = -1
Slope of AB × Slope of QC = -1
Slope of QC = (k - 4)/(h - 2)
4 × (k - 4)/(h - 2) = -1
(4k - 16)/(h - 2) = -1
4k - 16 = -h + 2
4k + h = 18 .......equation 1.
Similarly, we have the following:
Slope of BC × Slope of AH = -1
-3/2 × (k)/(h + 2) = -1
3k/(2h + 4) = 1
3k = 2h + 4
3k - 2h = 4 .......equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
8k + 2h = 36
3k - 2h = 4
11k = 40
k = 40/11.
For the value of h, we have:
h = -4k
h = -4 × (40/11)
h = -160/11
Therefore, the coordinates of the point of congruency of the altitudes (H) are (-160/11, 40/11).
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(sin alpha +cos alpha )2
Step-by-step explanation:
sin alpha^2 + 2sin alpha* cos alpha + cos alpha^2
sin alpha^2 + cos alpha^2 +2sin alpha* cos alpha
1+ 2sin alpha* cos alpha
1+sin2 alpha
ASAP HELP ME WITH THIS QUESTIONN
Answer:
inductive reasoning
Step-by-step explanation:
Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.
−22
–4
2
32
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Evaluate by substituting :
[tex]\begin{gathered} \boldsymbol{f(x)=-2x^2-3x+5; \ evaluate \ when \ x=-3} \\\boldsymbol{Write \ -3 \ everywhere \ you \ see \ and \ x :}\\\boldsymbol{f(-3)=-2(-3)^2-3(-3)+5}\\\boldsymbol{Evaluate \ using \ Order \ of \ Operations :}\\\boldsymbol{f(-3)=-2(9)+9+5= > -18+9+5= > -18+14= > -4}\end{gathered}[/tex]
Therefore, the answer is [tex]\LARGE\textbf{-4}[/tex].
I hope the answer - and steps - made sense to you !!
Happy Learning !!
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
I have 3 more then twice as many socks then keith she has 19 pairs of socks how many do keith have using algebra to solve this what is one step to take?
Answer:
40
Step-by-step explanation:
19*2 = 38 + 2 = 40
Answer:
Step-by-step explanation:
we have to get k by itself on one side of the equal sign. To do that we have to get rid of 3. To get rid of 3 we have to do the opposite. The opposite of +3 is -3 so we -3 on both sides. 19 - 3 = 16. So k = 16
k+3=19
-3 -3
k=16
Simplify the expression cos (tan-1(x/2)).
\cos (\tan \left( -1\right) (\frac{x}{2}))
c
o
s
(
t
a
n
(
−
1
)
(
2
)
)
Simplify
1
Combine multiplied terms into a single fraction
\cos (\tan \left( -1\right) \cdot \frac{x}{2})
c
o
s
(
t
a
n
(
−
1
)
⋅
2
)
\cos (\frac{\tan \left( -1\right) x}{2})
c
o
s
(
t
a
n
(
−
1
)
2
)
Solution
\cos \left( \frac{\tan \left( -1\right) x}{2}\right)
c
o
s
(
t
a
n
(
−
1
)
2
)
Answer:
Step-by-step explanation:
[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]
In 5-card poker, the number of outcomes favorable to an event E is given in the table. Find the
probability of being dealt four of a kind or a a straight.
The probability of being dealt four of a kind or a straight is
(Round to 6 decimal places.)
Event E
Royal flush
Straight flush
Four of a kind
Full house
Flush
Straight
Three of a kind
Two pairs
One pair
No pair
Total
# of Outcomes Favorable to E
4
36
624
3744
5108
10,200
54,912
123,552
1,098,240
1,302,540
2,598,960
The probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
In 5-card poker, find the probability of being dealt the following hand. Refer to the table.
From the table:
Total number of outcomes = 2598960
Total number of favorable outcomes = 624 + 10200 = 10824
The probability of being dealt four of a kind or a straight
P = 10824/2598960
P = 0.00416
In percentage:
P = 0.416%
Thus, the probability of being dealt four of a kind or a straight is 0.00416 or 0.416%.
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The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1. x –2 0 1 2 3 h(x) 0 –12 0 8 0 If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
Using the Factor Theorem, the equation of h(x) is given as follows:
h(x) = -2(x³ - 2x² - 5x + 6)
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x) = 0, the roots of h(x) are given as follows:
[tex]x_1 = -2, x_2 = 1, x_3 = 3[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
a = -12/6
a = -2.
Hence the function is given by:
h(x) = -2(x³ - 2x² - 5x + 6)
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When a lilac bush is planted, it is 24 inches tall. Each month, it grows 6 inches taller. How tall will It get over time?
Dependent variable: ______
Independent variable: ______
Equation: ______
Answer:
Dependent variable: time(months) or [tex]t[/tex]
Independent variable: 6
Step-by-step explanation:
[tex]h=24+6t[/tex]
(h=height)
Which expression represents the
number of reams of paper the company
produced during the second year?
The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)
What is the expression that represents the reams produced in the second year.The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.
In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, The number 5 x 10³ is equivalent to 500
Paper produced in the second year = paper produced in the first year x 5.6
(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]
4.704 x [tex]10^{9 + 1}[/tex]
= 4.704 x [tex]10^{10}[/tex]
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Find the solution of the differential equation that satisfies the given initial condition. dy/dx=x/y , y(0)=-1
Separating variables, we have
[tex]\dfrac{dy}{dx} = \dfrac xy \implies y\,dy = x\,dx[/tex]
Integrate both sides.
[tex]\displaystyle \int y\,dy = \int x\,dx[/tex]
[tex]\dfrac12 y^2 = \dfrac12 x^2 + C[/tex]
Given that [tex]y(0)=-1[/tex], we find
[tex]\dfrac12 (-1)^2 = \dfrac12 0^2 + C \implies C = \dfrac12[/tex]
Then the particular solution is
[tex]\dfrac12 y^2 = \dfrac12 x^2 + \dfrac12[/tex]
[tex]y^2 = x^2 + 1[/tex]
[tex]y = \pm\sqrt{x^2 + 1}[/tex]
and because [tex]y(0)=-1[/tex], we take the negative solution to accommodate this initial value.
[tex]\boxed{y(x) = -\sqrt{x^2+1}}[/tex]
help! giving brainlest to best answer!
Answer:
C...........................
Given: m space measured angle space C space equals space 76, a = 20, and b = 13. What is the length of c to the nearest tenth?
Based on the given parameters, the length of c is 8.0 units
How to determine the side length of c?The given parameters are
Angle c = 76 degrees
Side a = 20
Side b = 13
The length of c is then calculated using the following law of sines
c^2 = a^2 + b^2 - 2absin(C)
Substitute the known values in the above equation
So, we have
c^2 = 20^2 + 13^2 - 2 * 20 * 13 * sin(76)
Express 20^2 as 400
c^2 = 400 + 13^2 - 2 * 20 * 13 * sin(76)
Express 13^2 as 169
c^2 = 400 + 169 - 2 * 20 * 13 * sin(76)
Evaluate the product and sin(76)
c^2 = 400 + 169 - 520 * 0.9703
Evaluate the product
c^2 = 400 + 169 - 504.55
Evaluate the exponents
c^2 = 400 + 169 - 504.55
So, we have
c^2 = 64.45
Evaluate the square root
c = 8.0
Hence, the length of c is 8.0 units
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1+1-1(2)+1=?
A,0
B,1
C,2
D,3
Answer:
B. 1
Step-by-step explanation:
-1*2 = -2
-2+1 = -1
-1+1 = 0
0+1 = 1
A cannonball is shot straight upward with a velocity of 80 ft/sec. Its height after t seconds is given by f (t) = 80t - 16 t to the second power. Round your answers to 1 decimal place if necessary.
How high will the cannon ball go?
How many seconds will it take to reach this maximum height?
Check the picture below, so the ball's path is pretty much like so, and it reaches its hightest at its vertex, so
[tex]~~~~~~\textit{initial velocity in feet} \\\\ h(t) = -16t^2+v_ot+h_o \quad \begin{cases} v_o=\textit{initial velocity}&80\\ \qquad \textit{of the object}\\ h_o=\textit{initial height}&0\\ \qquad \textit{of the object}\\ h=\textit{object's height}&h\\ \qquad \textit{at "t" seconds} \end{cases} \\\\\\ f(t)=80t-16t^2\implies f(t)=-16t^2+80t+0 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-16}x^2\stackrel{\stackrel{b}{\downarrow }}{+80}x\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 80}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (80)^2}{4(-16)}\right) \implies \left( - \cfrac{ 80 }{ -32 }~~,~~0 - \cfrac{ 6400 }{ -64 } \right) \\\\\\ \left( \cfrac{5}{2}~~,~~100 \right)\implies \underset{~\hfill feet ~~ }{\stackrel{seconds\qquad }{\left( 2\frac{1}{2}~~,~~100 \right)}}[/tex]
On Wednesday, the temperature changes -3
∘
each hour for 10 hours. If the temperature was 12
∘
to begin with on Wednesday, what was the temperature after the 10 hours.
Answer:
-24 would be the temperature
Answer:
-24 BECAUSE I did all the math.
How do I graph the following set {x is an even number, -1≤x<12}
Step-by-step explanation:
Use this sort of layout, but where x will be an odd number, do not shade it. there should be a pattern of shaded segments followed by unshaded segments repeating
Jocelyn has a ladder that is 15 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 13.5 ft above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be less than 75°. Will the ladder be safe at this height? Show your work and equation to support your answer
By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.
Will the ladder be safe at this height?Notice that the ladder makes a right triangle with the wall.
Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft
If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.
Then we can use the relation:
sin(x) = (opposite cathetus)/(hypotenuse)
Then:
sin(x) = (13.5ft)/(15ft)
If we use the inverse sine function on both sides, we get:
Asin(sin(x)) = Asin( 13.5ft/15ft)
x = Asin(13.5/15) = 64.2°
So the angle is less than 75°, which means that in fact, the ladder is safe.
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The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
The ski club has 44 members in all
What is population?
Population refers to the total number of items or individuals that form a group.
In this case, the population means the total number of all members in the Mogul Runners ski club.
What is sample?
Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.
We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.
25% of club members=11 members
divide both sides by 25%
25%/25% of club members=11/25% members
club members=44 members
The ski club has 44 members altogether as computed above.
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A bagel factory produced 300 bags of bagels. There were 7 bagels in each bag. How many
bagels did the factory produce?
bagels
Find the value of b.
Step-by-step explanation:
The value of b will be 43° as it is vertically opposite angle.. !!