Answer:
There are 3 red marbles.
Step-by-step explanation:
The ratio of red marbles to blue marbles is 3:2, so for every two blue marbles there are three red marbles. This means that there are three red marbles for every four marbles in the bag. Therefore, if there are five marbles in the bag, there must be three red marbles and two blue marbles.
Let $m$ and $n$ be positive integers such that $m$ has exactly 5 positive divisors, $n$ has exactly 6 positive divisors, and $mn$ has exactly 14 positive divisors. How many distinct prime factors does $mn$ have
If [tex]A[/tex] is the set of positive divisors of [tex]m[/tex] and [tex]B[/tex] the set of positive divisors of [tex]n[/tex], then [tex]A\cup B[/tex] is the set of positive divisors of [tex]mn[/tex].
Use the inclusion/exclusion principle:
[tex]|A \cup B| = |A| + |B| - |A \cap B|[/tex]
where [tex]|\cdot|[/tex] denotes set cardinality (the number of elements the set contains). The set [tex]A\cap B[/tex] is the set of common divisors of [tex]m[/tex] and [tex]n[/tex]. Then
[tex]14 = 5 + 6 - |A\cap B| \implies |A\cap B| = 3[/tex]
so that [tex]m[/tex] and [tex]n[/tex] share 3 divisors [tex]d_1,d_2,d_3[/tex]; let [tex]k=d_1d_2d_3[/tex] be their product. They must be prime
This means we can write
[tex]m = p_1 p_2 k[/tex]
[tex]n = p_3 p_4 p_5 k[/tex]
[tex]\implies mn = p_1 p_2 p_3 p_4 p_5 k^2 = p_1 p_2 p_3 p_4 p_5 {d_1}^2 {d_2}^2 {d_3}^2[/tex]
so that [tex]mn[/tex] has up to 8 distinct prime factors.
I really need help!!!
Solve each equation by using the Quadratic Formula. Round to the nearest tenth
if necessary.
72. x²-25=0
75. 2r²+r- 14 = 0
73. r²+25=0
76. 5v^2-7v = 1
Answer:
72. 5
73. -5
74.r =2.40753645…,−2.90753645
75. v =1.53066238…,−0.13066238
Step-by-step explanation:
Please help with this and pls give all steps!!!
Answer:
No solutions.
Step-by-step explanation:
Problem:
Solve y−4x=−3;y=4x+7
Steps:
I will solve your system by substitution.
y=4x+7;−4x+y=−3
Step: Solve y=4x+7 for y:
Step: Substitute 4x+7 for y in −4x+y=−3:
−4x+y=−3
−4x+4x+7=−3
7=−3(Simplify both sides of the equation)
7+−7=−3+−7(Add -7 to both sides)
0=−10
Answer:
No solutions.
Answer:
No solutions
Step-by-step explanation:
It is easiest to determine whether the equations are consistent by putting both of them in the same form.
Adjusting the formThe equation on the left is in "standard form." The one on the right is in "slope-intercept form." We can rewrite either one of them to put it into the other form.
Rewriting the left equation to slope-intercept form, we have ...
y = 4x -3 . . . . . . . add 4x to both sides
Comparing this to the right equation ...
y = 4x +7
we see that the slopes are the same, and the intercepts are different. These equations describe parallel lines. Parallel lines can never meet, so cannot have any point in common. The equations are inconsistent and have no solution.
Rewriting the right equation to standard form, we have ...
y -4x = 7 . . . . . . . subtract 4x from both sides
Comparing this to the left equation ...
y -4x = -3
we see that the coefficients are the same, but the constants are different. There can be no values of x and y that will satisfy both equations. Any values that make the terms have one sum cannot also make them have a different sum.
There are no solutions.
On a quiz show, Linda won $10 less than three times as much as Charlie. If Linda won $800, how much did Charlie win?
Using a system of equations, it is found that Charlie won $270.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount earned by Linda.Variable y: Amount earned by Charlie.Linda won $10 less than three times as much as Charlie, hence:
x = 3y - 10
Linda won $800, hence the amount won by Charlie is found as follows:
800 = 3y - 10
3y = 810
y = 810/3
y = 270
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Suppose a batch of metal shafts produced in a manufacturing company have a variance of 9 and a mean diameter of 207 inches. If 72 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches
The probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches is 39.54%.
Given mean diameter of 207, variance=9, sample size of 72.
We have to calculate the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches.
The sample mean may be greater than or less than from population mean than 0.3 inches.
Either greater than 207+0.3=207.3 inches,
Smaller =207-0.3=206.7
Since the normal distribution is symmetric these probabilities are equal. So we find one of them and multiply by 2.
Probability of being less than 206.7
P value of z when X=206.7. So
Z=(X-μ)/s
=(206.7-207)/0.35
=-0.3/0.35
=-0.857
p value =0.1977
Probability of differing from population mean greater than 0.3 inches=2*0.1977
=0.3954
=39.54%
Hence the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.3 inches is 39.54%.
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For the arithmetic sequence beginning with the terms {7, 11, 15, 19, 23 ...}, what is the sum of the first 31 terms?
a.)
1827
b.)
1950
c.)
2077
d.)
2208
Step-by-step explanation:
here a= 7 ,d=4
then S31= 31/2(7+7+30*4)= 31/2(14+120)= 31/2(134)= 31*67= 2077
hope it helps
The sum of the first 31 terms is 2077.
What is Arithmetic Sequence?An arithmetic sequence is one in which each phrase grows by adding or subtracting some constant k. In contrast, in a geometric sequence, each term grows by dividing/multiplying some constant k.
We have,
Sequence: {7, 11, 15, 19, 23 ...}
First term = 7
Common difference, d= 11- 7 = 4
Now, the sum of first 31 st term of sequence
= 31/2 [ 2(7) + (31-1)4]
= 31/2 [ 14 + 120]
= 31/2 x 134
= 31 x 67
= 2077
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Heheh be svdbtjdjsbddb
The question is on the picture below
Answer: 54
Step-by-step explanation:
By the inscribed angle theorem, angle ZXY measures half of 108 degrees, which is 54 degrees.
In the triangle below, what is the measure of
Answer:
D. 30°
Step-by-step explanation:
QP and QR have the same length "8" , therefore, the triangle is an isosceles triangle. Opposite angles are congruent.
- ∠R = ∠P
- ∠R = 30°
-----------------------------
What is the value of X
Answer:
x = 10
Step-by-step explanation:
BF is two times AX so
2 ( 2x+10) = 5x+10
4x + 20 = 5x + 10
x = 10
Find the altitude of this equilateral triangle - geometry
Answer:
4√3.
Step-by-step explanation:
If the height is h then
tan 60 = h / (1/2*8)
tan 60 = h/4
h = 4 tan 60
= 4 * √3.
PLEASE HELP ME WITH THIS QUESTION TT ITS A EQUIVALENT QUESTION!!!
thank you!
Answer: [tex]\boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}[/tex] (choice D)
You have the correct answer.
=====================================================
Work Shown:
[tex]\frac{2}{\text{x}} + \frac{3}{\text{x}-1}\\\\\frac{2(\text{x}-1)}{\text{x}(\text{x}-1)} + \frac{3\text{x}}{\text{x}(\text{x}-1)}\\\\\frac{2\text{x}-2}{\text{x}^2-\text{x}} + \frac{3\text{x}}{\text{x}^2-\text{x}}\\\\\frac{2\text{x}-2+3\text{x}}{\text{x}^2-\text{x}}\\\\ \boldsymbol{\frac{5\text{x}-2}{\text{x}^2-\text{x}}}\\\\[/tex]
--------
Explanation:
The idea I used is that we cannot add the fractions unless the denominators are the same. The denominators x and (x-1) lead to the lowest common denominator, aka LCD, of [tex]\text{x}(\text{x}-1) = \text{x}^2 - \text{x}[/tex]. We multiply the denominators together to get the LCD.
The first original fraction [tex]\frac{2}{\text{x}}[/tex] is missing (x-1) in the denominator. This is why I multiplied top and bottom by (x-1) in the 2nd step. Similarly, the fraction [tex]\frac{3}{\text{x}-1}[/tex] is missing an x out front to get to x(x-1). This is why I multiplied top and bottom of that fraction by x.
After we get the denominators to be the same, we can then add the numerators like any other algebraic expression. The denominator stays the same the entire time.
It's similar to how [tex]\frac{2}{7} + \frac{3}{7} = \frac{2+3}{7} = \frac{5}{7}[/tex] has the numerators add like you'd expect while the denominator stays at 7 the entire time.
You can think of it like this: "2 sevenths + 3 sevenths = 5 sevenths" or "2s+3s = 5s" for short. The term "sevenths" is effectively a unit such as cm or meters. We must have common units if we want to add them.
Greetings. As a beginner, I'm struggling a bit to learn calculus. May I know what is the derivative of x to the power 4 step by step?
Thanks in advance!
If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate [tex]x^4[/tex].
We have
[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x+h)^4 - x^4}h[/tex]
Expand the numerator using the binomial theorem, then simplify and compute the limit.
[tex]\dfrac{d}{dx} x^4 = \displaystyle \lim_{h\to0} \frac{(x^4+4hx^3 + 6h^2x^2 + 4h^3x + h^4) - x^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} \frac{4hx^3 + 6h^2x^2 + 4h^3x + h^4}h \\\\ ~~~~~~~~ = \lim_{h\to0} (4x^3 + 6hx^2 + 4h^2x + h^3) = \boxed{4x^3}[/tex]
In general, the derivative of a power function [tex]f(x) = x^n[/tex] is [tex]\frac{df}{dx} = nx^{n-1}[/tex]. (This is the aptly-named "power rule" for differentiation.)
what is the value of x when (fog)(x)=-8
The value of x when (f o g)(x) = -8 is 3
How to solve for x?The composite function is given as:
(f o g)(x) = -8
The above is calculated as:
(f o g)(x) = f(g(x))
So, we have:
f(g(x)) = -8
From the table, we have:
f(-4) = -8
This means that:
g(x) = -4
From the ordered pair, we have:
g(x) = -4 when x = 3
Hence, the value of x is 3
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The value of x when (f o g)(x) = -8 is 3
How to solve for x?
The composite function is given as:
(f o g)(x) = -8
The above is calculated as:
(f o g)(x) = f(g(x))
So, we have:
f(g(x)) = -8
From the table, we have:
f(-4) = -8
This means that:
g(x) = -4
From the ordered pair, we have:
g(x) = -4 when x = 3
Hence, the value of x is 3
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A full can of milk weighs 70 pounds. If exactly half of the milk is poured out, it weighs 38 pounds. How much does the empty can weigh?
Answer:
6 pounds
Step-by-step explanation:
Let the can weigh x pounds
Let the milk weigh y when full, therefore half is [tex]\frac{y}{2}[/tex]
Now we for 2 simultaneous equations:
[tex]x + y =70[/tex] ....(i)
[tex]x+ \frac{y}{2}= 38[/tex] .... (ii)
we solve by eliminating the x in both equation throug subtraction
[tex]x - x + y- \frac{y}{2} =70-38\\y- \frac{y}{2} = 32\\\frac{y}{2} = 32\\y=2(32)\\y=64\\x+y=70\\x+64=70\\x=6[/tex]
2) Express 34m 5cm 6mm in millimeteres
Answer:
34079 millimeters
Step-by-step explanation:
__________________________________
I assume you mean millimeters, but
34 m = 34000 millimeter4 cm = 4 centimeters = 40 millimeter5 mm = 5 millimeterAll together adds up to 79 millimeter
34000 + 40 + 5 = 34079 mm
__________________________________
Hope this helped
(Edit) Sorry I didn't see meters
I’m having issues with finding the restriction of the equation in the photo
Answer:
x = 9
Step-by-step explanation:
Restricted value of the expressionSimplify the equation.Set the denominator to 0.Solve and find the solution.The solution is the restricted value of the equation.[tex]\sf \dfrac{(x +7)(x+8)}{(x -9(x + 6)} \ \div \ \dfrac{(x+8)(x - 2)}{(x+ 6)(x - 2)} =\dfrac{(x +7)(x+8)}{(x -9)*(x +6)}*\dfrac{(x + 6)(x - 2)}{(x +8 )(x - 2)}[/tex]
[tex]\sf =\dfrac{x +7}{x - 9}[/tex]
x - 9 = 0
x = 9
If we plugin x = 9, then the denominator would become 0 and hence the expression will become undefined.
So, x = 9 is the restricted value of the expression.
which vectors are unit vectors?
The unit vectors are u = {1, 1}. Option C
What are unit vectors?Unit vectors can be defined as vector with magnitude of 1.
It is important to note that a unit vector is a vector quantity. Vector quantities are known to have magnitude and direction.
They are represented with the sign 'u'
Thus, the unit vectors are u = {1, 1}. Option C
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What is the equation of the function that is graphed as line a?
Answer:
Option 1
Step-by-step explanation:
The equations in the options are in the slope-intercept form (y= mx +c, where m is the slope and c is the y-intercept).
In the graph, the line cuts through the y-axis at y= -2. Thus, c= -2 and the 2nd option can be eliminated.
The slope can be found using the formula below.
[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
Let's choose 2 points on the line: (0, -2) and (-2, 4)
Slope
[tex]=\frac{4-(-2)}{-2-0}[/tex]
[tex]=\frac{4+2}{-2}[/tex]
[tex]=\frac{6}{-2}[/tex]
= -3
The equation of the line is thus y= -3x -2.
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https://brainly.com/question/14200719Solve: (6x2 + 5x + 1) + (x + 2).
Answer:
6x+6x2+3
Step-by-step explanation:
6x2+5x+1+x+2
Combine 5x and x to get 6x.
6x2+6x+1+2
Add 1 and 2 to get 3.
6x2+6x+3
The simplified form of the expression (6x² + 5x + 1) + (x + 2) is 6x^2 + 6x + 3.
To solve the expression (6x² + 5x + 1) + (x + 2)
we need to combine like terms.
First, let's remove the parentheses:
6x² + 5x + 1 + x + 2
Next, we combine like terms:
6x² + (5x + x) + (1 + 2)
Simplifying further:
6x^2 + 6x + 3
Therefore, the simplified form of (6x² + 5x + 1) + (x + 2) is 6x² + 6x + 3.
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Which statement correctly explains how to prove △ABC∼△DEF?
Answer:
A
Step-by-step explanation:
calculate the ratios AB/DE BC/EF AND AC/DF。their ratios are 1/2
Answer:
Step-by-step explanation:
the first because the ratio is always from a small to a large triangle, and it is right, the second is wrong, the sides are not congruent, the third is also wrong, the last ratio is wrong
The scale on a map is 1 cm : 6 km. If two cities are 13 cm apart on the map, what is the actual distance between the cities?
Answer:
78 km!
Step-by-step explanation:
13 cm * 6 km per cm = 78 km in actual distance
ASAP please
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is followed by a--------------.
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.
Translation is the movement of a point either up, down, left or right on the coordinate plane.
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a translation followed by a rotation.
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Convert 2077 to base eight
To convert 2077₁₀ to base eight is 4035₈
How to convert 2077 to base 8?Since 2077 is in base 10, to convert it to base 8, we successively divide it by 8 and keep the remainder. We divide until we have zero as the dividend then count the remainder from bottom to top.
So, to convert 2077 to base 8, we have
2077 ÷ 8 = 259 r 5
259 ÷ 8 = 32 r 3
32 ÷ 8 = 4 r 0
4 ÷ 8 = 0 r 4
So, counting the remainders from bottom to top, we have 4035₈
So, 2077₁₀ = 4035₈
So, to convert 2077₁₀ to base eight is 4035₈
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-4,12-5-22,24-100,37 ordenar de menor a mayor
Answer: 24 - 100, 12 - 5 - 22, -4, 37
Step-by-step explanation:
Simplificar:
-4 = -4
12 - 5 - 22 = -15
24 - 100 = -76
37 = 37
Ordenar de menor a mayor:
-76, -15, -4, 37
\/
24 - 100, 12 - 5 - 22, -4, 37
Use any method to solve the equation. If necessary, round to the nearest hundredth.
7x^2-16x=8
Hello,
Answer:
S = { -0,42 ; 2,71 }
Step-by-step explanation:
7x² - 16x = 8 ⇔ 7x² - 16x - 8 = 0
a = 7 ; b = -16 ; c = -8
Δ = b² - 4ac = (-16)² - 4 × 7 × (-8) = 480 > 0
x₁ = (-b - √Δ)/2a = (16 - √480)/14 ≈ -0,42
x₂ = (-b + √Δ)/2a = (16 + √480)/14 ≈ 2,71
Answer:
The two answers:
2.707778736
0.42206445
Step-by-step explanation:
Here is the equation:
[tex] {7x}^{2} - 16x = 8[/tex]
Take away the 8 from the right hand side, so that we are left with this quadratic equation:
[tex] {7x}^{2} - 16x - 8 = 0[/tex]
This equation is too complex to solve with the factorizing method, so let's use the quadratic formula, which is as follows:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
In this equation, a = 7, b = -16, and c = -8. So let's substitute in:
[tex]x = \frac{-( - 16) \pm \sqrt{ { - 16}^{2} - 4 \times 7 \times - 8}}{2 \times 7}[/tex]
[tex]x = \frac{ - ( - 16) \pm \sqrt{256 + 224} }{14}[/tex]
[tex]x = \frac{ 16 \pm \sqrt{480}}{14}[/tex]
And let's work out the two possible answers:.
2.707778736
0.42206445
3
Which expression is equivalent to x-2
O
O O
O
2x-8
13–5x
-5r-8
2x-8
-5x-4
x-2
13–5x
2x-8
-
5
2- 4
x-2
?
Step-by-step explanation:
[tex] = \frac{ \frac{3}{x - 2} - 5 }{2 - \frac{4}{x - 2} } [/tex]
[tex] = \frac{ \frac{3 - 5.(x - 2)}{x - 2} }{ \frac{2.(x - 2) - 4}{x - 2} } [/tex]
[tex] = \frac{ \frac{3 - 5.(x - 2)}{ \cancel{x - 2}} }{ \frac{2.(x - 2) - 4}{ \cancel{x - 2} }} [/tex]
[tex] = \frac{3 - 5.(x - 2)}{2.(x - 2) - 4} [/tex]
[tex] = \frac{3 - 5x + 10}{2x - 4 - 4} [/tex]
[tex] = \frac{ - 5x + 13}{2x - 8} [/tex]
[tex] = \frac{13 - 5x}{2x - 8} [/tex]
The answer is D.
The equivalent value of the expression is A = ( 13 - 5x ) / ( 2x - 8 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
In an equation, the expressions on either side of the equals sign are called the left-hand side (LHS) and the right-hand side (RHS), respectively. The equals sign (=) indicates that the two expressions have the same value, and that the equation is true for certain values of the variables involved.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. It typically consists mathematical operations, such as addition, subtraction, multiplication, division, and exponentiation.
Given data ,
Let the equation be represented as A
Now , the value of A is
[tex]A = \frac{\frac{3}{x-2}-5}{2\:-\:\frac{4}{x-2}}[/tex]
On simplifying , we get
[tex]A = =\frac{\frac{-5x+13}{x-2}}{2-\frac{4}{x-2}}[/tex]
On further simplification , we get
[tex]A = =\frac{\frac{-5x+13}{x-2}}{\frac{2x-8}{x-2}}[/tex]
Therefore , the value of A is A = ( 13 - 5x ) / ( 2x - 8 )
Hence , the equation is A = ( 13 - 5x ) / ( 2x - 8 )
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PLEASE HELP< GEOMTREY SUCKS!!!!!!!!!
Answer:
The measure of angle DCB = 125
Step-by-step explanation:
This is because angle ACD and angle DCB are supplementary.
Supplementary angles are two angles with a sum of 180 degrees, and we know these angles are supplementary by the fact that angle ACB = 180 degrees.
There are 480 students in a school.
and
1
of the students wear glasses.
5
How many of the students do not wear glasses
Answer:
96 students
Step-by-step explanation:
I am not exactly sure if this question is talking about a 1:5 ratio, but that's what I am assuming. To get 96, you need to replace the 5 with 480 because the problem seems to mean 1 to every 5 people wear glasses. Next, you do 480/5 to get the number on the left side of the ratio. You get 96 when you do that. I am a little confused with the question because it isn't exactly formatted correctly, but this is what I am guessing. Hope this helps!
Help I need this urgently!!!!