[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p-\frac{3}{4}=4 } \end{gathered}$}}[/tex]
Add 3/4 to both sides.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=4+\frac{3}{4} } \end{gathered}$}}[/tex]
Convert 4 to the fraction 16/4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16}{4} +\frac{3}{4} } \end{gathered}$}}[/tex]
Since 16/4 and 3/4 have the same denominator, add their numerators to add them together.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{16+3}{4} \longmapsto \ \ Add } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{5}{8}p=\frac{19}{4} } \end{gathered}$}}[/tex]
Multiply both sides by 8/5, the reciprocal of 5/8.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19}{4}\times\left(\frac{5}{8}\right) } \end{gathered}$} }[/tex]
Multiply 19/4 by 8/5 (to do this, multiply the numerator by the numerator and the denominator by the denominator).
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{19\times8}{4\times5 }\longmapsto \ Multiply } \end{gathered}$}}[/tex]
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} } \end{gathered}$}}[/tex]
We reduce the fraction 152/20 to its minimum expression by extracting and canceling 4.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{p=\frac{152}{20} \ \ \longmapsto \ p=\frac{152\div4}{20\div4}=\frac{38}{5} } \end{gathered}$}}[/tex]
Therefore, the answer is option C.22% of the squirrels in Cititon Park are gray. What is the probability that, in a random sample of 322
squirrels, fewer than 71 are gray squirrels? Use a normal approximation to compute your answer.
Round your answer to 4 decimal places.
The probability is 0.4841 .
Probability theory is the name of the branch of mathematics that deals with probability.
Although there are many ways to interpret the concept of probability, probability theory approaches it in a formal mathematical manner by articulating it through a set of axioms. These axioms typically formalize probability in terms of a probability space, which connects a sample space of possible outcomes to a measure that accepts values between 0 and 1. Statistical mechanics or sequential estimation are two examples of how probability theory approaches can be used to describe complicated systems when only a piece of their state is known. A significant achievement in twentieth-century physics was the description of the probabilistic nature of physical events at the atomic scale in terms of quantum mechanics.Given n = 322
p = 0.22
We know that from probability
μ = n × p = 0.22 ×322 = 70.84
σ = √(p × n×(1-p)) = 7.43
Now (P < 71) = P<70.84
Solving we get
P(z<-0.045)
= 0.48405
Therefore the probability is 0.4841
To learn more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Find (f - g)(x)
f(x) = 3x² - 2x
g(x) = 9x²2 - x + 7
A. -6x²-x-7
B. 6x²-x+7
C. 12x²-x-7
D. -6x²-3x - 7
The solution to the given function is (f-g)(x) = -6x² - x - 7.
What is a function?
Function, in mathematics, an expression, rule, or law that defines a relationship between : one variable (the independent variable) and another variable (the dependent variable).
A function is an equation with a single solution for y for each value of x. Each input of a particular type receives exactly one output when using a function. Instead of y, a function is frequently named f(x) or g(x). When x equals 2, we should determine our function's value because f(2) says to do so.
Given: f(x) = 3x² - 2x
g(x) = 9x² -x + 7
To find: ( f - g )(x)
thus (f-g)(x)= 3x² - 2x - ( 9x² - x + 7)
(f-g)(x) = -6x² - x - 7
To know more about function visit:
https://brainly.com/question/13461298
#SPJ9
What is the product?
1/2•(12 64)
(78 30)
Graph the line that is perpendicular to the line
7x+8y= 16 and passes through the
point (7, 2).
The general equation of the line is 7x+8y−65=0 when the line equation is 7x+8y=16 and the point is (7,2) and is perpendicular to the given line.
What is line?A line is a one-dimensional figure with no width and only length. A line is made up of a series of points that extend in opposite directions indefinitely. Two points in a two-dimensional plane determine it. Collinear points are two points that are located on the same line.
What is equation of line?A straight line's general equation is y = mx + c, where m is the gradient and y = c is the value at which the line intersects the y-axis. This number c is known as the y-axis intercept.
here, the given equation is 7x+8y=16 and point is (7,2).
by the relation y = mx + c we will find the value of slope for the line.
8y=-7x+16
y=(-7/8 ) x+16
on comparing relation,
m=[tex]\frac{-7}{8}[/tex]
y=mx+b
b=y1-m.x1
b=2-(-7/8).7
b=65/8
y=(-7/8)x+65/8
final equation,
7x+8y=65
The required equation of the line is 7x+8y=65 for the given point and line.
to know more about line equation,
https://brainly.com/question/28867398
#SPJ13
30 60 90° triangles find the measure of the missing two sides for each figure below leave answer and rationalize and simple light form
Given : 30 60 90 triangle as shown in the following figure :
As shown : the hypotenuse of the triangle = 28√5
The side length opposite to the angle 30 =
[tex]\frac{1}{2}\cdot28\sqrt[]{5}=14\sqrt[]{5}[/tex]The side length opposite to the angle 60 =
[tex]\frac{\sqrt[]{3}}{2}\cdot28\sqrt[]{5}=\frac{28}{2}\sqrt[]{3\cdot5}=14\sqrt[]{15}[/tex]3х2 + 14х — 49 = 0solve for x
The given expression 3x^2 +14x-49=0
we will de factorization tos solve for x
[tex]\begin{gathered} 3x^2+14x-49=0 \\ 3x^2-7x+21x-49=0 \\ (3x^2-7x)+(21x-49)=0 \\ \text{Taking x common from (}3x^2-7x)=x(3x-7) \\ \text{Taking 7 common from }(21x-49)=7(3x-7) \\ (3x^2-7x)+(21x-49)=0 \\ x(3x-7)+7(3x-7)=0 \\ \text{Taking (3x-7) common} \\ (3x-7)(x+7)=0 \\ \text{ Thus, for} \\ \text{(3x-7)=0} \\ 3x=7 \\ x=\frac{7}{3} \\ \text{and for (x+7)=0} \\ x+7=0 \\ x=-7 \end{gathered}[/tex]The value of x is -7 and 7/3
Answer : x = -7 and x = 7/3
Pls help I’ll mark brainliest im too tired for this
Answer:
309.8$
Step-by-step explanation:
450.60 - 35.20*4
= 309.8
:]
Convert 21,510 ft to mi
Answer:
4.0738636
Step-by-step explanation:
Writing an equation of a hyperbola give me the Foci and vertices
Given the Foci of the hyperbola:
[tex]\begin{gathered} (-1,-9) \\ (-1,9) \end{gathered}[/tex]And the Vertices:
[tex]\begin{gathered} (-1,-3) \\ (-1,3) \end{gathered}[/tex]You can plot the Foci on a Coordinate Plane:
Notice that the blue line represents the Vertical Transverse Axis. Then, the equation has this form:
[tex]\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1[/tex]You need to find the Center using the Midpoint Formula, in order to find the Midpoint between the Foci and the Midpoint between the vertices:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]- For the Foci:
[tex]M=(\frac{-1-1}{2},\frac{-9+9}{2})=(-1,0)[/tex]- For the Vertices:
[tex]M=(\frac{-1-1}{2},\frac{-3+3}{2})=(-1,0)[/tex]Therefore:
[tex]\begin{gathered} h=-1 \\ k=0 \end{gathered}[/tex]Now you need to find "a". This is the distance from the center to the vertices:
[tex]a=3-0=3[/tex]Find "b" with this formula:
[tex]b^2=c^2-a^2[/tex]Knowing that "c" is the distance from the Foci to the center:
[tex]c=9[/tex]You get:
[tex]b^2=9^2-3^2=72[/tex]Therefore, you can write this equation:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]Hence, the answer is:
[tex]\frac{y^2}{9}-\frac{(x+1)^2}{72}=1[/tex]E Match the corresponding congruent parts.(G.6)(6 point) DE DF / A Lc ZB EF
By definition:
Congruent figures in geometry are identical in shape and size.
This means that two figures are congruent with each other even if they are rotated, flipped or trasnlated as long as they have the identical shape and size.
For example, look at the following picture
We notice that the triangle has the same size and shaped, hence they are congruent. Furthermore we can say that the side BC is congruent to the side ZY and so on.
Match the two lines that are parallel and the two lines that are perpendicular. Then, match the equations.
Step-by-step explanation:
A and C are parallel. equations G and E.
B and D are perpendicular (standing at a right angle = 90° to each other). equations F and H.
parallel means that both lines have the same slope.
the slope is the factor a of x when the equations look like
y = ax + b (slope-intercept form)
or
y - y1 = a(x - x1) (point-slope form)
"a" being the slope, b being the y-intercept (the y- value when x = 0), (x1. y1) being a point on the line.
the slope is specified as ratio (y coordinate difference / x coordinate difference) when going from one point to another.
the perpendicular slope to y/x is the upside down ratio and the sign is flipped.
e.g. the perpendicular slope to 5/4 is -4/5.
equation E is already in point-slope form.
the slope is 2/3, and the point (-9, -2) must be on the line.
only one line goes through the point (-9, -2) : C.
equation H is already in slope-intercept form.
the slope is 3/2, and the y-intercept is 5, meaning the line goes through the point (0, 5).
only one line goes through that point : D
equation F
2x + 3y = -21
3y = -2x -21
y = (-2/3)×x - 7
the slope is -2/3, which is perpendicular to 3/2 (equation H).
the y-intercept is -7, meaning the line goes through the point (0, -7).
only one line goes through that point : B
equation G
-2x + 3y = -6
3y = 2x - 6
y = (2/3)×x - 2
the slope is 2/3 (parallel to equation E).
the y-intercept is -2, meaning the line goes through the point (0, -2).
only one line goes through that point : A
Consider the steps James uses to solve the equation 2(x – 10) = 24. Equation: 2(x - 10) = 24 Step 1: 2x - 10 = 24 Step 2: 2x = 34 Step 3: x = 17 In which step, if any, did James make an error? A. Step 1 B. Step 2 C. Step 3 D. James did not make an error.
In the steps that James uses to solve the given equation he made a mistake:
We have:
[tex]2\cdot(x-10)=24\Rightarrow2x-20=24[/tex]James needed to apply the distributive property in the first step. However, he did not.
Therefore, James made an error in Step 1, that is, option A.
At a local restaurant, the amount of time that customers have to wait for their food isnormally distributed with a mean of 12 minutes and a standard deviation of 2minutes. Using the empirical rule, determine the interval of minutes that the middle99.7% of customers have to wait.
By the empirical rule 99.7% of the customers fall within the interval bounded by
[tex]\bar{x}-3\sigma\text{ and }\bar{x}+3\sigma[/tex]In this case,
[tex]\begin{gathered} \bar{x}=12\min \text{ and} \\ \sigma=2\min \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \bar{x}-3\sigma=12-3(2)=12-6=6\min s \\ \bar{x}+3\sigma=12+3(2)=12+6=18\min s \end{gathered}[/tex]Hence, the interval of minutes that the middle 99.7% of customers have to wait is given by
(6mins, 18mins)
Using the graph below, write two ordered pairs to show that the equation y = 15x represents the data.
By using the points (2, 30) and (4, 60) that we can see on the graph, we can see that the linear equation that models the data is:
y = 15*x
How to find the equation that models the data?A general linear equation is of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two points (x₁, y₁) and (x₂, y₂), the slope is given by:
a = (y₂ - y₁)/(x₂ - x₁)
In this case we can use two points that appear on the graph, I will use the first two ones:
(2, 30) and (4, 60)
Then the slope is:
a = (60 - 30)/(4 - 2) = 30/2 = 15
Thus, the line is of the form:
y = 15*x + b
To find the value of b we use the point (2, 30), replacing these values we get:
30 = 15*2 + b
30 = 30 + b
30 - 30 = b
0 = b
We conclude that the linear equation that models the data is y = 15*x
Learn more about linear equations:
https://brainly.com/question/28999997
#SPJ1
The perimeter of a rectangle is equal to 138. The width of the rectangle is 5 less than the length . What is the area the rectangle?
Step 1: Concept
Perimeter of a rectangle = 2( L + W)
L = length
W = width
Area of a rectangle = Lenght x Width
Step 2:
Given data
The perimeter of a rectangle = 138
Length L = m
Width W = m - 5
Step 3:
[tex]\begin{gathered} \text{Use the perimeter of the rectangle to find the length(L) and width(W).} \\ \text{Perimeter = 2(L + W)} \\ 138\text{ = 2(m + m - 5)} \\ 138\text{ = 2m + 2m - 10} \\ 138\text{ = 4m - 10} \\ \text{Collect similar terms} \\ 138\text{ + 10 = 4m} \\ 148\text{ = 4m} \\ m\text{ = }\frac{148}{4}\text{ = 37} \end{gathered}[/tex]Step 4:
Length = 37
Width = 37 - 5 = 32
Step 5:
Find the area
Area = length x width
Area = 37 x 32
Area = 1184
Final answer
Area of the rectangle = 1184
What is a valid conclusion that can be reached by reading the graph?A.Joel and Nancy own 62 cards when you add their cards together.B.Joel and Nancy own more cards than Jim when you add their cards together.C.Nancy and Ricardo own more cards than Jim when you add their cards together.D.Tina owns 350 cards.
Answer:
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
Explanation:
Taking into account the graph, we can conclude the following:
Nancy and Ricardo own more cards than Jim when you add their cards together
This is because, Nancy and Ricardo have bars with heights that are greater than 40, when we add their cards, we will get a bar with a height greater than 80, and 80 is greater than the height of Jim's bar.
Therefore, the answer is
C. Nancy and Ricardo own more cards than Jim when you add their cards together.
kind of confused with this whole probability concept, i just need help with these here
Solution
For this case we have 0-9 possible digits (10) and 4 spaces for the code
Part a
The number of ways are using the multiplication principle:
10x9x8x7= 5040
Part b
p= 1/5040
Part c
If digits can be repeated we have this:
10x10x10x10= 10000
the wholesale price for a pair of shoes is $5.50. A certain department store marks up the wholesale price by 40%. Find the price of shoes in the department store.
EXPLANATION
Price of shoes = $5.50
Markup= 40%
Let's call x to the unknown final price.
The markup percentage relationship is given by the following formula:
[tex]\text{Markup =( }\frac{Selling\text{ Price}-\text{Cost Price}}{\text{Cost Price}})\cdot100[/tex]Replacing terms:
[tex]\text{40}=(\frac{x-5.5}{5.5})\cdot100[/tex]Multiplying both sides by 5.5:
[tex]40\cdot5.5=(x-5.5)\cdot100[/tex]Dividing both sides by 100:
[tex]\frac{40\cdot5.5}{100}=x-5.5[/tex]Adding 5.5 to both sides:
[tex](\frac{40\cdot5.5}{100})+5.5=x[/tex]Simplifyng the fraction:
[tex]2.2+5.5=x[/tex]Adding numbers:
[tex]\text{7}.7\text{ = x}[/tex]Switching sides:
[tex]x=7.7[/tex]Answer: The final price of the shoes in the deparment store is $7.7
What is the product of 840 and 4.6 x 102 expressed in scientific notation?
We can rewrite the expression:
[tex]840\times4.6\cdot10^2=8.4\cdot10^2\times4.6\cdot10^2[/tex]The product is,
[tex](8.4\times4.6)(10^2\times10^2)=(38.64)(10^{2+2})=38.64\times10^4[/tex]Sketch a graph of 6 x + 4 y = 4
The graph of 6x + 4y = 4 can be sketched as shown in the image attached below.
How to Sketch the Graph of a Linear Equation?A linear equation can be expressed in standard form as Ax + By = C, where A, B, and C are integers. Also, it can be rewritten in slope-intercept form as y = mx + b, where b is the y-intercept and m is the slope of the equation.
In order to graph an equation, we can easily determine what the slope (m) and the y-intercept (m) of the graph would be when we rewrite the equation in slope-intercept form.
Given the equation in standard form as, 6x + 4y = 4, rewrite it in slope-intercept form:
6x + 4y = 4
4y = -6x + 4
y = -6x/4 + 4/4
y = -3/2x + 1
This means that the slope of the graph you'd sketch will be -3/2, and the line must intercept the y-axis at 1, because the y-intercept is 1.
The graph is shown below.
Learn more about the graph of an equation on:
https://brainly.com/question/14323743
#SPJ1
2+4-2÷3 please help
A easy way to operate fractions is convert the integer in a fraction, to operate fractions with the same denominator:
[tex]6\cdot\frac{3}{3}-\frac{2}{3}=\frac{18}{3}-\frac{2}{3}=\frac{16}{3}[/tex]The Sugar Sweet Company is going to transport its sugar to market. It will cost $5500 to rent trucks plus $125 for each ton of sugar transported. The total cost,
C (in dollars), for transporting n tons is given by the following.
C=125n+5500
Answer the following questions.
(a) What is the total cost of transporting 11 tons?
(b) If the total cost is $8125, how many tons is the company transporting?
pythagorean theorem
Answer:
7.75 units squared
Step-by-step explanation:
10. Sydney wants to buy soda and juice for her birthday party. A bottle of soda costs $1.99 each and a jug of juice costs $2.49 each. If Sydney has $30, what equation could be used to find how many soda bottles and how many jugs of juice she can purchase? let x = let y = Equation
ANSWER
1.99x + 2.49y = 30
EXPLANATION
A bottle of soda costs $1.99 each and a jug of juice costs $2.49.
Sydney has $30.
Let x be the number of bottles of soda she can get.
Let y be the number of jugs of juice that she can buy.
This means that the cost of x bottles of soda is:
1.99 * x = $1.99x
This also means that the cost of y jugs of juice is:
2.49 * y = $2.49y
The total cost must be equal to $30, so this means that the total cost of bottles of soda and jugs of juice she can purchase is:
1.99x + 2.49y = 30
That is the equation that represents it.
. Fritz spent two days last week writing his report and
another three days this week. In the last ten working
days, what fraction of the time has he been working
on his report?
Answer:
1/2
Step-by-step explanation:
5/10 which is the same as 1/2
Mr. Rodriquez is purchasing throphies for each trophies for each child that play little ldag
From the information provided, Mrs Rodriguez wants to spend nothing more than $7.00 per trophy. That means she can spend less than $7.00 if she has to, but she cannot spend anything above that amount.
Therefore, the correct answer is option 2, and that is;
5 trophies for $30.00
With other options given, she would be spending above $7.00 per trophy
Add.
Your answer should be an expanded polynomial in
standard form.
(-4b³ + b − 1) + (6b - 6) =
Answer:
-4b^3 + 7b - 7
Step-by-step explanation:
We have to look at terms which look like each other, for example 1b and 6b.
We can add and subtract terms which have the same degree of b.
In this question, we can safely add -1 and -6, and also b and 6b,
which gives us (-4b^3 + b - 1 ) + 6b - 6) = -4b^3 + (1+6)b +( -1 - 6) = -4b^3 + 7b - 7
The three remaining terms all have different degrees of b's (respectively 3, 1, 0), so we can't add those up any further, which tells us that this is the right answer.
Answer:
Step-by-step explanation:
I don't understand this at all.
Answer:
P1V1T2
T1= _______
P2V2
Step-by-step equation:
Create your own thought experiment explaining why a negative divided by a negative is a positive.
Dividing two negative numbers results in a positive number.A negative number divided by a negative number produces a positive result since two negatives equal a positive.
Explaining why a negative divided by a negative is a positive
The quotient is positive when two negative values are divided.The same guidelines apply to multiplication. Divided by another negative integer, a negative number always yields a positive number.divided equally by.The solution cannot be or any other negative number because it is positive. Divide two negative numbers, and you'll always get a positive number as the result.For instance, dividing -4 by -2 yields 2.The negatives cancel out when both numbers are negative, hence the outcome is always a positive number. Consider that you are taking part in a game that uses red and black chips.You will win one dollar (+1) at the end of the game for each black chip you have.You must pay one dollar for every red chip you possess.Assume that at some time throughout the game you have numerous bags of black chips and several bags of red chips. These chips are currently bundled together in bags of five.You make $15 if someone offers you three bags of black chips.(3)(5)=15.You lose 15 bucks if someone steals three of your bags of black chips.(-3)(5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You lose $15 if someone gives you three bags of red chips.(3)(-5)=-15.You make 15 bucks if someone steals three of your bags of red chips.(-3)(-5)=15.The crucial concept is that negative numbers signify variations rather than totals.Saying that you have four slices of bread is illogical.However, it makes logical to state that since you had 4 slices of bread, the new number of slices you possess is 4.
To learn more about number experiment refer
https://brainly.com/question/8972272#
#SPJ13
PLS HELP WILL MARK BRAINLIEST
Answer:
l = [tex]\frac{P-2w}{2}[/tex]
Step-by-step explanation:
P = 2l + 2w ( subtract 2w from both sides )
P - 2w = 2l ( isolate l by dividing both sides by 2 )
[tex]\frac{P-2w}{2}[/tex] = l