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Related Questions
the sum of two numbers is 18 . the difference of the two numbers is -2 find the numbers
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a + b = 18
a - b = -2
2a = 16
a = 8
8 + b = 18
b = 10
Factor out the coefficient of the variable. The expression 2.2x +4.4 factored is
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The measure of arc XZ is 28° what is the measure of XYZ
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Angle XYZ is marked in blue
It turns out that angle XYZ is exactly half the measure of arc XZ. This is due to the inscribed angle theorem. Angle XYZ is an inscribed angle that cuts off, or subtends, arc XZ.
measure of arc XZ = 28 degrees
measure of angle XYZ = (1/2)*(measure of arc XZ)
measure of angle XYZ = (1/2)*(28 degrees)
measure of angle XYZ = 14 degrees
Answer: D) 14 degrees
The Perez family has a rectangular fish tank how much water will the tank hold if it's length is 3 feet, its width is 2 feet and its height is 3 feet
A) NONE
B) 18 cubic feet
C) 3 cubic feet
D) 6 cubic feet
E) 9 cubic feet
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answer
B) 18 cubic feet
You've got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?
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x minutes : 60 problems
10 * 60/8 = 150/2 = 75 minutes for 60 problems
solve 6[4x(72-63)divided3]
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whats the nearest tenth to -61 square root
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that is, i=√-1
so we can write
[tex]\sqrt{-61}=(\sqrt{-1})(\sqrt{61})=(i)(\sqrt{61})[/tex] [tex] \sim (i)(7.81) \sim 7.8i[/tex]
the √(-61) is a complex number √61i
But if you wish to find the value of an irrational and imaginary number, I will give you the approximate answer.
[tex] \sqrt{-61} \to \sqrt{-1*61} \to \sqrt{-1} * \sqrt{61} \to i* \sqrt{61} \to i*7,81024...\: \boxed{\approx 7.8i}[/tex]
6-1. let x have a poisson distribution with a mean of 4. find (a) p(2≤x≤5). (b) p(x≥3). (c) p(x≤3).
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[tex]f_X(x)=\dfrac{e^{-4}4^x}{x!}[/tex]
So,
a. [tex]\mathbb P(2\le X\le5)=\dfrac{e^{-4}4^2}{2!}+\cdots+\dfrac{e^{-4}4^5}{5!}\approx0.6936[/tex]
b. [tex]\mathbb P(X\ge3)=\dfrac{e^{-4}4^3}{3!}+\dfrac{e^{-4}4^4}{4!}+\cdots\approx0.7619[/tex]
c. [tex]\mathbb P(X\le3)=\dfrac{e^{-4}4^0}{0!}+\cdots+\dfrac{e^{-4}4^3}{3!}\approx0.4335[/tex]
6578 divided 34
20\5
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Answer:
263.56 :)
Step-by-step explanation:
A school conference room can seat a maximum of 83 people. The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements. If each student must bring a parent with them, what is the maximum number of students that can attend each meeting?
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Answer:
The maximum number of students that can attend each meeting is:
40
Step-by-step explanation:
A school conference room can seat a maximum of 83 people.
The principal and two counselors need to meet with the school’s student athletes to discuss eligibility requirements.
Let there be x students,there will be x parents
that means x+x+3≤83
Subtracting both sides by 3,we get
2x≤80
dividing both sides by 2,we get
x≤40
Hence, the maximum number of students that can attend each meeting is:
40
An object's position is given by x(t) = 5 + 10 t 2. what is its acceleration after 5 s
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The acceleration after 5 seconds is 20 m/s^2.
Explanation:To find the acceleration, we need to take the second derivative of the position function.
x(t) = 5 + 10t^2
Taking the derivative with respect to time, we get:
v(t) = 20t
Taking the derivative again, we get the acceleration:
a(t) = 20
Therefore, the acceleration after 5 seconds is 20 m/s^2.
Which three statements would produce the truth value F when p is true and q is false?
A. p -> q
B. ~p/\~q
C. p->~q
D. q\/~p
C. p/\~q
please help
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Answer with Step-by-step explanation:
p is true then ~p is false.
q is false then ~q is true.
A. p -> q
if p is true and q is false then this gives false truth value.
Hence, here truth value is F
B. ~p/\~q
if any one of them is false then it gives false truth value.
Hence, here truth value is F(since,~p is false)
C. p->~q
true statement implies a true statement hence, truth value will be true
Hence, here truth value is T(p true implies ~q true)
D. q\/~p
if any one of them is true then compound statement is true.
Hence, here truth value is F(since, ~p and q both are false)
E. p/\~q
if both true then compound statement is also true.
Hence, here truth value is T(since p and ~q both are true)
if 2 pounds of strawberries cost 4.50 how much would 3 pounds cost
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Find the missing number of each unit rate
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6/2 = 3/1
12/4 = 3/1
if the last on is negative it would -24/8 = -3/1 if positive 3/1 hope this helps remember you would reduce your fraction
12/4 reduces to 3/1
Can you do the remaining problems?
You make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over. What fractional portion of the original bowl of salad does each friend receive?
Answers
Answer:
[tex]\frac{2}{3x}[/tex]
Where, x = total friends
Step-by-step explanation:
Given,
The part of the salad has eaten = [tex]\frac{1}{3}[/tex]
Total part of the salad = 1,
Thus, the remaining part of the salad = original part - part has eaten
[tex]=1-\frac{1}{3}[/tex]
[tex]=\frac{3-1}{3}[/tex]
[tex]=\frac{2}{3}[/tex]
If there are x friends,
Then the portion of the original bowl of salad received by each friend
[tex]=\frac{\text{Remaining part}}{\text{Total friends}}[/tex] [tex]=\frac{2}{3x}[/tex]
determine the quadratic function of f whose graph is given. The vertex is (1,-3) and the y-intercept is -2
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and we know where the vertex is at. Let's assume a vertical parabola, in which case the squared variable is the "x".
[tex]\bf \qquad \textit{parabola vertex form}\\\\ \begin{array}{llll} \boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\ x=a(y-{{ k}})^2+{{ h}} \end{array} \qquad\qquad vertex\ ({{ h}},{{ k}})\\\\ -------------------------------\\\\ vertex \begin{cases} h=1\\ k=-3 \end{cases}\implies y=a(x-1)^2-3 \\\\\\ \textit{now, we also know that } \begin{cases} x=0\\ y=-2 \end{cases}\implies -2=a(0-1)^2-3 \\\\\\ 1=a(-1)^2\implies \boxed{1=a}\qquad thus\implies \begin{cases} y=1(x-1)^2-3\\ \textit{or just}\\ y=(x-1)^2-3 \end{cases} [/tex]
Solve for the distance between (522, 1322) and (9000, -1337) to the third decimal.
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What is the volume of a paperback book 21 cm tall, 12 cm wide, and 3.5 cm thick?
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The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm².
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
Volume has units of cube example meter³,cm³, etc.
Given a paperback book shape as cuboid
Length(tall) = 21 cm
Width(wide) = 12cm
Height (thick) = 3.5 cm
The volume of the cuboid is given as
Volume = length × height × width.
Volume = 21 × 12 × 3.5
Volume = 882 cm²
Hence" The volume of a cuboid is given as length × width × height thus the volume of the paperback book will be 882 cm²".
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Find the volume of a rectangular block of ice 3 feet by 6 1/3 and 1 1/2 feet
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Final answer:
The volume of the rectangular block of ice is 85.5 cubic feet. This was found by converting the mixed numbers into improper fractions, then multiplying the length, width, and height together using the formula volume = length × width × height.
Explanation:
To find the volume of a rectangular block of ice with the given dimensions, we simply need to multiply the length, width, and height together. The formula to calculate volume is Volume = length × width × height. First, however, we need to convert the mixed numbers into improper fractions so we can multiply them easily.
The length is given as 6 1/3 feet, which can be converted to an improper fraction: (6 × 3) + 1 = 19/3 feet. The height is given as 1 1/2 feet, which is (1 × 2) + 1 = 3/2 feet.
Now, to find the volume, we multiply these dimensions with the width, which is 3 feet.
Volume = (19/3) feet × 3 feet × (3/2) feet
The feet × feet × feet will give us cubic feet.
Multiplying these together:
Volume = (19 × 3 × 3) / (3 × 2) cubic feet
Volume = 171/2 cubic feet or 85.5 cubic feet
Thus, the volume of the block of ice is 85.5 cubic feet.
A geologist have two rocks on a scale that weighs 2 1/2 lbs together rock a was 1/7 of a the total weight how much did rock a weight
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By using the given fraction of rock 'a' against the total weight of two rocks, we can find that rock 'a' weighs approximately 0.357 lbs.
Explanation:The student's question involves calculating the weight of a rock, given as a fraction of a total weight. In this case, they are talking about a scenario where a geologist uses a scale to weigh two rocks together, with a total weight of 2 1/2 lbs, and rock 'a' is specified to be 1/7 of this total weight. To determine the weight of rock 'a', we simply divide the total weight by 7.
So, 2 1/2 lbs is equivalent to 2.5 lbs (since 1/2 is the same as 0.5). To find the weight of rock 'a', we take this total weight and perform the operation: 2.5 ÷ 7 = 0.357 lbs.
Therefore, rock 'a' weighs approximately 0.357 lbs. Remember, this is an estimation because the weight of the rock is being given as a fraction of the total weight, and actual weights can vary based on factors such as density and volume.
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Determine whether or not the vector field is conservative. if it is conservative, find a function f such that f = ∇f. (if the vector field is not conservative, enter dne.) f(x, y, z) = ye−xi + e−xj + 2zk
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[tex]\nabla\times\mathbf f(x,y,z)=-2e^{-x}\,\mathbf k[/tex]
so this vector field is not conservative.
- - -
Another way of determining the same result: We want to find a scalar function [tex]f(x,y,z)[/tex] such that its gradient is equal to the given vector field, [tex]\mathbf f(x,y,z)[/tex]:
[tex]\nabla f(x,y,z)=\mathbf f(x,y,z)[/tex]
For this to happen, we need to satisfy
[tex]\begin{cases}f_x=ye^{-x}\\f_y=e^{-x}\\f_z=2z\end{cases}[/tex]
From the first equation, integrating with respect to [tex]x[/tex] yields
[tex]f_x=ye^{-x}\implies f(x,y,z)=-ye^{-x}+g(y,z)[/tex]
Note that [tex]g[/tex] *must* be a function of [tex]y,z[/tex] only.
Now differentiate with respect to [tex]y[/tex] and we have
[tex]f_y=-e^{-x}+g_y=e^{-x}\implies g_y=2e^{-x}\implies g(y,z)=2ye^{-x}+\cdots[/tex]
but this contradicts the assumption that [tex]g(y,z)[/tex] is independent of [tex]x[/tex]. So, the scalar potential function does not exist, and therefore the vector field is not conservative.
To ascertain if a vector field is conservative or not, you need to calculate the curl of the field or integrate over the components of the vector field. If the curl is zero, it's conservative. If the curl isn't zero or an integral doesn't exist, the field is not conservative.
Explanation:To determine if the vector field f(x, y, z) = ye−xi + e−xj + 2zk is conservative, we need to find if there exists a function f such that f is the gradient (denoted by ∇) of f. This can be done by checking if the cross product of the vector field is equal to zero, which signifies that the field is conservative.
First, we calculate the curl (∇ x F) of the vector field, which gives us the derivatives of the field components. If the curl is zero, then the vector field is conservative. If it is not zero, this indicates that the vector field is non-conservative.
Alternatively, we can integrate over the components of the vector field to try and find a potential function. If an integral exists, then we can say that the vector field is conservative.
However, if it fails these conditions, then the vector field is not conservative and the function f does not exist for it (dne). Thus, in the case where the vector field is not conservative, enter 'dne'.
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WILL GIVE BRAINEST
categorize the graph as liner increase...
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Allison drive 30 mph through the city and 55 mph on the New Jersey Turnpike she drove 90 miles from battery Park to the Jersey shore how much of the time was city driving if she needs about 1.2 hours on the turnpike
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Determine whether the given function is linear. if the function is linear, express the function in the form f(x)
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The given function [tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex] is indeed linear, and it can be expressed as f(x) = x in the standard linear form.
Let's break down the analysis of the given function[tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex].
1. Initial Expression:
[tex]\[ f(x) = \frac{5}{5} \cdot x \][/tex]
2. Simplify the Fraction:
[tex]\[ \frac{5}{5} \][/tex] simplifies to 1, so the expression becomes:
[tex]\[ f(x) = 1 \cdot x \][/tex]
3. Multiplication by 1:
Multiplying any value by 1 does not change the value, so the expression further simplifies to:
f(x) = x
4. Linear Form:
The function is now in the form f(x) = ax + b with a = 1 and b = 0:
[tex]\[ f(x) = 1 \cdot x + 0 \][/tex]
Therefore, the given function [tex]\(f(x) = \frac{5}{5} \cdot x\)[/tex] is indeed linear, and it can be expressed as f(x) = x in the standard linear form.
Complete Question: Determine whether the given function is linear. if the function is linear, express the function in the form f(x) = ax + b. (if the function is not linear, enter not linear.)
f(x) = 5 / 5 x
Suppose e(x) = 3 and e[x(x − 1)] = 27.5. (a) what is e(x2)? [hint: first verify that e[x(x − 1)] = e[x2 − x] = e(x2) − e(x).]
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For what values of a and b is the line 2x + y = b tangent to the parabola y = ax2 when x = 2?
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The first derivative of y = ax^2 represents the slope of the tangent line to the curve of y = ax^2. Here, dy/dx = 2ax. When x = 2, dy/dx = 2a(2) = 4a.
The point of tangency is (2,y), where y = a(2)^2, or y=4a; thus, the point of tangency is (2,4a). The equation of the tangent line to y=ax^2 at (2,4a) is found by (1) differentiating y=ax^2 with respect to x, (2) letting x = 2 in the result: dy/dx = 2ax => dy/dx (at 2,4a) = 2a(2) = 4a
The line 2x + y = b is supposed to be tangent to y = ax^2 at (2,4a).
The slope of 2x + y = b is found by solving 2x + y = b for y:
y = b - 2x => slope m = -2
Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b. We know that 2x + y = b, so if x=-2 and y=-8,
2(-2) + [-8] = b = -4 - 8 = -12
Thus, the equation of the parabola is y = ax^2 = (-1/2)x^2.
a = -2 and b = -8 are the required a and b values.
The equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.
What is the slope of the tangent line?The first derivative of y = ax² that represents the slope of the tangent line to the curve of y = ax² .
Here, dy/dx = 2ax.
When x = 2,
dy/dx = 2a(2) = 4a.
The point of tangency is (2,y), where y = a(2)², or y=4a;
thus, the point of tangency is; (2, 4a).
The equation of the tangent line to y=ax² at (2,4a)
Now differentiating y=ax² with respect to x,
dy/dx = 2ax
dy/dx (at 2,4a) = 2a(2) = 4a
The line 2x + y = b is tangent to y = ax² at (2,4a).
The slope of 2x + y = b can be found by solving 2x + y = b for y:
y = b - 2x
Slope m = -2
Thus, dy/dx = 4a = - 2, and thus a = -2/4, or a = -1/2. All we have to do now is to find the value of b.
We know that 2x + y = b, then if x=-2 and y=-8,
2(-2) + [-8] = b = -4 - 8 = -12
Thus, the equation of the parabola is y = ax² = (-1/2)x² where a = -2 and b = -8 are the required values of a and b.
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What is the common difference for the arithmetic sequence?
4.7, 6, 7.3, 8.6, 9.9,...
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Amanda can jog 18 miles in 5 hours. At this rate, how many miles can Amanda jog in 4 hours?
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__ __
5 4
x = 18•4 / 5
72/5 = 14.4 final answer
we know that
Amanda can jog [tex]18[/tex] miles in [tex]5[/tex] hours
so
by proportion
Find the number of miles that Amanda can jog in [tex]4[/tex] hours
[tex]\frac{18}{5} \frac{miles}{hours} =\frac{x}{4} \frac{miles}{hours} \\ \\5*x=18*4 \\ \\x=72/5 \\ \\ x=14.4\ miles[/tex]
therefore
the answer is
[tex]14.4\ miles[/tex]
Given f(x) = x^2 - 10x + 22, what is the range of f?
Answers
For a parabola that opens up, it is everything greater than the vertex.
If the vertex is (h,k) then the range is y >= k.
Vertex can be found using completing the square:
[tex]x^2 -10x +22 \\ \\ (x^2 -10x + (\frac{-10}{2})^2) +22 - (\frac{-10}{2})^2 \\ \\ (x^2 -10x+25) +22-25 \\ \\ (x-5)^2 - 3[/tex]
(h,k) = (5,-3) ------> Range is y >= -3
Vertex may also be found using formula [tex]h = \frac{-b}{2a} [/tex]
a = 1, b = -10, c = 22
[tex]h = \frac{10}{2} = 5[/tex]
[tex]k = 5^2 - 10(5) +22 \\ \\ k = 25 -50+22 \\ \\ k = -3[/tex]
------> Range is y >= -3
f(x)=x2-10x+22 domain of f
Answer: all real numbers
Range of F
Answer: y> -3
MARIA WALKED 4.035 KILOMETERES. WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?
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Answer:
[tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]
Step-by-step explanation:
Given : MARIA WALKED 4.035 KILOMETERS.
To Find :WHAT IS 4.035 WRITTEN IN AS EXPANDED FORM ?
Solution :
Number = 4.035
The numbers after decimals when read from first to last has positions tenth , hundredth , thousandth and so ...
The number before the decimal part has positions ones , tens , hundreds and so on when read from last to first
Now 4 is at ones place
0 is at tenth place
3 is at hundredth place
5 is at thousandth place
So, Expanded form : [tex](4 \times 1)+(3 \times \frac{1}{100})+(5 \times \frac{1}{1000})[/tex]