Given:
Total Number of ways = 54
Number of body styles = 3
Number of engine choices = 2
Let's find the number of colors available.
To find the number of colors available, we have:
Number of ways = Number of body styles x Number of engine choices x Number of colors
54 = 3 x 2 x c
Where c represent the available number of colors.
Let's find c.
54 = 3 x 2 x c
54 = 6c
Divide both sides by 6:
[tex]\begin{gathered} \frac{54}{6}=\frac{6c}{6} \\ \\ 9=c \\ \\ c=9 \end{gathered}[/tex]Therefore, there are 9 colors available to select from.
ANSWER:
9
Solve each system of equations algebraically.[tex]y = {x}^{2} + 4 \\ y = 2x + 7[/tex]
From the problem, we two equations :
[tex]\begin{gathered} y=x^2+4 \\ y=2x+7 \end{gathered}[/tex]Since both equation are defined as y in terms of x, we can equate both equations.
[tex]\begin{gathered} y=y \\ x^2+4=2x+7^{} \end{gathered}[/tex]Simplify and solve for x :
[tex]\begin{gathered} x^2+4=2x+7 \\ x^2-2x+4-7=0 \\ x^2-2x-3=0 \end{gathered}[/tex]Factor completely :
[tex]\begin{gathered} x^2-2x-3=0 \\ (x-3)(x+1)=0 \end{gathered}[/tex]Equate both factors to 0 then solve for x :
x - 3 = 0
x = 3
x + 1 = 0
x = -1
We have two values of x, x = 3 and -1
Substitute x = 3 and -1 to any of the equation, let's say equation 2 :
For x = 3
y = 2x + 7
y = 2(3) + 7
y = 6 + 7
y = 13
One solution is (3, 13)
For x = -1
y = 2x + 7
y = 2(-1) + 7
y = -2 + 7
y = 5
The other solution is (-1, 5)
The answers are (3, 13) and (-1, 5)
0.0032% in fraction
Recall that the x% in fraction form is:
[tex]\frac{x}{100}\text{.}[/tex]Therefore 0.0032% as a fraction is:
[tex]\frac{0.0032}{100}=\frac{\frac{32}{10000}}{100}\text{.}[/tex]Simplifying the above result we get:
[tex]\frac{\frac{32}{10000}}{100}=\frac{32}{100\times10000}=\frac{1}{31250}\text{.}[/tex]Answer:
[tex]\frac{1}{31250}[/tex]use the half angle identity to find the exact value of the trigonomic expression. given 0
Given a right angle triangle:
we need to find the measure of the angle θ
As shown:
The opposite side to the angle θ = 24
The adjacent side to the angle θ = 45
So,
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent}=\frac{24}{45} \\ \\ \theta=\tan ^{-1}\frac{24}{45}=28.0725 \\ \\ \sin \frac{\theta}{2}=\sin \frac{28.0725}{2}=\sin 14.036=0.2425 \end{gathered}[/tex]so, the answer will be sin θ/2 = 0.2425
HELP ME PLS!!!!!!!
Total consumption of fruit juice in a particular country in 2006 was about 2.15 billion gallons. The population of that country in 2006 was 400 million. What was the average number of gallons of fruit juice consumed per person in the country in 2006? using the per person amount from this problem, about how many gallons would your class consume?
Answer:
5.375 gallons/personStep-by-step explanation:
Total consumption of fruit juice in 2006:
2.15 billion gallonsThe population of the country:
400 million people.Average consumption of fruit juice per person in 2006 was:
2.15 billion / 400 million = 2.15 × 10⁹ / 400 × 10⁶ = 21.5 × 10⁸ / 4 × 10⁸ = 21.5 / 4 = 5.375 gallons/personTo find how many gallons of fruit juice would your class consume multiply the average consumption by the number of your class mates.
The volume of a square-based rectangular cardboard box needs to be at least 1000cm^3. Determine the dimensions that require the minimum amount of material to manufacture all six faces. Assume that there will be no waste material. The Machinery available cannot fabricate material smaller than 2 cm in length.
We have to find the dimensions of a box with a volume that is at least 1000 cm³.
We have to find the dimensions that require the minimum amount of material.
We can draw the box as:
The volume can be expressed as:
[tex]V=L\cdot W\cdot H\ge1000cm^3[/tex]The material will be the sum of the areas:
[tex]A=2LW+2LH+2WH[/tex]Since the box is square-based, the width and length are equal and we can write:
[tex]L=W[/tex]Then, we can re-write the area as:
[tex]\begin{gathered} A=2L^2+2LH+2LH \\ A=2L^2+4LH \end{gathered}[/tex]Now, we have the area expressed in function of L and H.
We can use the volume equation to express the height H in function of L:
[tex]\begin{gathered} V=1000 \\ L\cdot W\cdot H=1000 \\ L^2\cdot H=1000 \\ H=\frac{1000}{L^2} \end{gathered}[/tex]We replace H in the expression for the area:
[tex]\begin{gathered} A=2L^2+4LH \\ A=2L^2+4L\cdot\frac{1000}{L^2} \\ A=2L^2+\frac{4000}{L} \end{gathered}[/tex]We can now optimize the area by differentiating A and then equal the result to 0:
[tex]\begin{gathered} \frac{dA}{dL}=2\frac{d(L^2)}{dL}+4000\cdot\frac{d(L^{-1})}{dL} \\ \frac{dA}{dL}=4L+4000(-1)L^{-2} \\ \frac{dA}{dL}=4L-\frac{4000}{L^2} \end{gathered}[/tex][tex]\begin{gathered} \frac{dA}{dL}=0 \\ 4L-\frac{4000}{L^2}=0 \\ 4L=\frac{4000}{L^2} \\ L\cdot L^2=\frac{4000}{4} \\ L^3=1000 \\ L=\sqrt[3]{1000} \\ L=10 \end{gathered}[/tex]We now can calculate the other dimensions as:
[tex]W=L=10[/tex][tex]H=\frac{1000}{L^2}=\frac{1000}{10^2}=\frac{1000}{100}=10[/tex]Then, the dimensions that minimize the surface area for a fixed volume of 1000 cm³ is the length, width and height of 10 cm, which correspond to a cube (all 3 dimensions are the same).
Answer: the dimensions are length = 10 cm, width = 10 cm and height = 10 cm.
slope= 2; point on the line (-2,1) in slope intercept form I know y=m*x+b but all I know is 2 would be m
y=2x+5
1) Since we were told the slope is m=2, one point on the line (-2,1), and the slope-intercept form is:
[tex]y=mx+b[/tex]2) The next step is to find the value of "b", the y-intercept. So, let's pick that point, the slope, and plug them into the Slope-Intercept form:
[tex]\begin{gathered} y=mx+b,m=2,(-2,1) \\ 1=2(-2)+b \\ 1=-4+b \\ 1+4=b \\ b=5 \end{gathered}[/tex]3) Now that we know the y-intercept (b), we can write the function's rule as
[tex]y=2x+5[/tex]Solve the following equations. (You may leave your answer in terms of logarithms or you can plug your answer into a calculator to get a decimal approximation.)
Given the equation:
[tex]200(1.06)^t=550[/tex]We divide each side by 200:
[tex]\begin{gathered} \frac{200}{200}(1.06)^t=\frac{550}{200} \\ 1.06^t=2.75 \end{gathered}[/tex]Now, we take the natural logarithm:
[tex]\begin{gathered} \ln (1.06^t)=\ln (2.75) \\ t\cdot\ln (1.06)=\ln (2.75) \\ \therefore t=\frac{\ln (2.75)}{\ln (1.06)} \end{gathered}[/tex]Please help I'm not sure what should I substitute the variable (x) by
From the given table, the quadratic model is given by
[tex]y=1.2x^2+13x+504.3[/tex]which corresponds to option B.
The general quadratic model is given by
[tex]y=Cx^2+Bx+A[/tex]and we need to find the constants A, B and C. They are given by
and
For instance, the variance for x, denoted by S_xx is given by
[tex]S_{x\times}=(0-20)^2+(10-20)^2+(20-20)^2+(30-20)^2+(40-20)^2[/tex]where x is the variable which corresponds to the "years since 1970" and the number 20 in each parenthesis is the mean of the this variable, that is
[tex]\bar{x}=\frac{0+10+20+30+40}{5}=20[/tex]Now, the variance S_xy is given by
how would u decide if 3/5 or 59% is greater?
SOLUTION
Step 1 : One of the easiest ways to determine which one of the quantities is greater is by expressing the quantities as a decimal.
[tex]\begin{gathered} \frac{3}{5}\text{ = 0.6} \\ \\ 59\text{ \% = 0.59} \end{gathered}[/tex]Step 2: From the two quantities expressed as decimals, we can see that :
[tex]\frac{3}{5}\text{ is greater.}[/tex]CONCLUSION :
[tex]\frac{3}{5}\text{ is greater.}[/tex]Which number line shows point 3 point B ar -1.5 point C at 1 1/2 and point D which is opposite of point A
∵ Point A located at 3, then we will refuse answers B and D because
point A on them located at -3
∵ POint D is the opposite of point A
∴ Point D must locate at -3
∵ In figure A point D located at -3, point B located at -1.5, and
point C located at 1 1/2
∴ The number line in answer A is the correct answer
∴ The answer is figure A
Question 16
Given AEFHAGFH below, what is the measure of GFH?
F
21.6°
E<
(6x - 12)° H
G
1 pts
The most appropriate choice for congruency of triangles will be given by-
[tex]\angle GFH =68.4^{\circ}\\[/tex]
What is congruency of triangles?
Two triangles are said to be congruent if all the corrosponding sides and the corrosponding angles of the triangle are equal.
There are five axioms of congruency. They are -
SSS axioms, SAS axioms, ASA axiom, AAS axiom, RHS axiom.
Here,
[tex]\Delta EFH \cong \Delta GFH[/tex] [Given]
[tex]\angle E = \angle G = 21.6^{\circ}[/tex] [Corrosponding parts of congruent triangles are congruent]
[tex]\angle GFH[/tex] = 180 - (90 + 21.6) [Sum of the three angles of a triangle is 180°]
[tex]\angle GFH = 180 - 111.6\\\angle GFH =68.4^{\circ}\\[/tex]
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I need help answering the questions for person 2 on my group assignment
The equation for the relation of sides of triangle can be obtained by similar triangle property.
Consider triangle ABC and triangle DBE.
[tex]\begin{gathered} \angle CAB=\angle EDA\text{ (Each angle is right angle)} \\ \angle CBA=\angle EBD\text{ (common angle)} \\ \Delta CBA\cong\Delta EBD\text{ (By AA similarity condition)} \end{gathered}[/tex]Determine the ratio of corresponding sides of simillar triangle.
[tex]\frac{CB}{EB}=\frac{BA}{BD}=\frac{CA}{ED}[/tex]Thus similar triangle property is used to set up the equation.
Using pH=-log{H3O+}, what is pH for 3.4 X 10^-4 ?
The value of the pH for pH=-log{H3O+} is found as 3.47.
What is defined as the pH?The pH of aqueous or some other liquid solutions is a quantitative measure of their acidity or basicity. The concentration of hydrogen ion, which normally ranges between around 1 and 10∧14 gram-equivalents per litre, is converted into a number between 0 and 14. The concentration of hydrogen ion in pure water, which really is neutral (nor acidic and neither alkaline), is 10∧7 gram-equivalents per litre, corresponding to a pH of 7. A solution with such a pH less than 7 is classified as acidic, while one with pH greater than 7 is classified as basic, or alkaline.For the given equation,
pH = - log [H3O+]
and , H3O+ = 3.4 X 10^-4
The, the pH will be estimated as;
pH = - log [ H3O+]
pH = - log [ 3.4 x10 ^-4]
pH = - [log 3.4 + log 10^-4]
pH = - [0.53 + (-4)]
pH = -[-3.47]
pH = 3.47
Thus, the value of the pH is found as 3.47.
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a rectangular prisim has a volume of 80cm cubed it has a length of 2cm and a width of 5cm. What is the prisms height?
rectangular prism volume is ,
[tex]\begin{gathered} V=l\times b\times h \\ 80=2\times5\times h \\ h=\frac{80}{10} \\ h=8\text{ cm } \end{gathered}[/tex]Determine the vertex and the axis of symmetry based on the equation, y =-12 -8x - 36
Solution
Determine the vertex and the axis of symmetry based on the equation:
[tex]y=-x^2-8x-36[/tex]Therefore the correct answer is Option A
if a ray QT bisects
EXPLANATION
If a ray QT bisects
(3x - 5) + (x+1) = 180 [By the Linear Pair Theorem]
Removing the parentheses:
3x - 5 + x + 1 = 180
Grouping like terms:
3x + x + 1 - 5 = 180
Adding like terms:
4x -4 = 180
Adding +4 to both sides:
4x = 180 + 4
Adding numbers:
4x = 184
Dividing both sides by 4:
x = 184/4
Simplifying:
x=46
Now, we need to compute the resulting angles:
m m
As QT bisects
47/2 = 23.5 degrees
The answer is 23.5°
How does g(t) = 4t change over the interval t = 3 to t = 4?
Over the interval t = 3 to t = 4, g(t) increases.
The increasing factor (f) is computed as follows:
[tex]f=\frac{g(4)}{g(3)}[/tex]where g(4) is g(x) at t = 4, and g(3) is g(x) at t = 3. Substituting with the formula of g(t) and evaluating each expression, we get:
[tex]\begin{gathered} f=\frac{4^4}{4^3} \\ f=\frac{4\cdot4^3}{4^3} \\ f=4 \end{gathered}[/tex]Then, g(t) increases by a factor of 4
Determine if the side lengths could form a triangle. Use an inequality to prove the answer. Inequality must be used.
The side lengths given form a triangle
Explanation:Let the lengths of the sides of the triangle be "a", "b" and "c"
For the length to form sides of a triangle, the sum of any two sides of the triangle must be greater than the third as shown:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]Given the sides of the triangle as 34km, 27km, and 58km
Let a = 34km, b = 27km and c = 58km
Substituting these values in the expression above to check if it is true:
[tex]\begin{gathered} 34+27=61>58 \\ 34+58=92>27 \\ 27+58=85>34 \end{gathered}[/tex]Since the inequality expression supports the theorem above, hence the side lengths given form a triangle
help me solve the volume of the cylinder? 20 ft x 17 ft
Remember that the formula for the volume of a cylinder is:
[tex]V=\pi r^2h[/tex]Where:
• r, is the ,radius, of the base
,• h ,is the height of the cylinder
Notice that the base has a diameter of 20 ft. Therefore, the radius is 10 ft.
Using this data and the formula, we get that:
[tex]\begin{gathered} V=\pi(10^2)(17) \\ \rightarrow V=5340.71 \end{gathered}[/tex]The volume of the cylinder is:
[tex]2540.71ft^3[/tex]its composition of fractions in pre-calculus.I know how to do these types of questions, im just not sure how u would set it up if there are 2 x's in one of the equations.
Answer:
(f o g)(x) = x
Explanation:
Given f(x) and g(x) defined below:
[tex]\begin{gathered} f(x)=\frac{1-x}{x} \\ g(x)=\frac{1}{1+x} \end{gathered}[/tex]The composition (f o g)(x) is obtained below:
[tex]\begin{gathered} (f\circ g)(x)=f\lbrack g(x)\rbrack \\ f(x)=\frac{1-x}{x}\implies f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)} \end{gathered}[/tex]Substitute g(x) into the expression and simplify:
[tex]\begin{gathered} f\lbrack g(x)\rbrack=\frac{1-g(x)}{g(x)}=\lbrack1-g(x)\rbrack\div g(x) \\ =(1-\frac{1}{1+x})\div(\frac{1}{1+x}) \\ \text{ Take the LCM in the first bracket} \\ =\frac{1(1+x)-1}{1+x}\div\frac{1}{1+x}\text{ } \\ \text{Open the bracket} \\ =\frac{1+x-1}{1+x}\div\frac{1}{1+x}\text{ } \\ =\frac{x}{1+x}\times\frac{1+x}{1}\text{ } \\ =x \end{gathered}[/tex]Therefore, the composition (f o g)(x) is x.
The vertex of the parabola below is at the point
SOLUTION
The equation of a parabola in a vertex form is given
since the parabola is on the x-axis.
[tex]\begin{gathered} x=a(y-h)^2+k \\ \text{Where } \\ \text{Vertex}=(h,k) \end{gathered}[/tex]From the diagram given, we have
[tex]\text{vertex}=(-4,-2)[/tex]Substituting into the formula above, we have
[tex]\begin{gathered} x=a(y-h)^2+k \\ h=-4,k=-2 \end{gathered}[/tex]We have
[tex]\begin{gathered} x=(y-(-2)^2-4 \\ x=(y+2)^2-4 \end{gathered}[/tex]Since the parabola is a reflection from the parent function, then
[tex]a=-2[/tex]The equation of the parabola becomes
[tex]x=-2(y+2)^2-4[/tex]Answer; x = -2(y + 2)^2-4
For what values of a are the following expressions true?/a+5/=-5-a
Explanation:
The expression is given below as
[tex]|a+5|=-5-a[/tex]Concept:
We will apply the bsolute rule below
[tex]\begin{gathered} if|u|=a,a>0 \\ then,u=a,u=-a \end{gathered}[/tex]By applying the concept, we will have
[tex]\begin{gathered} \lvert a+5\rvert=-5-a \\ a+5=-5-a,a+5=5+a \\ a+a=-5-5,a-a=5-5 \\ 2a=-10,0=0 \\ \frac{2a}{2}=\frac{-10}{2},0=0 \\ a=-5,0=0 \end{gathered}[/tex]Hence,
The final answer is
[tex]a\leq-5[/tex]Steve has been training for a 5-mile race. Before the race, he predicts he will finish in 42minutes. He actually finishes the race in 40 minutes. What is the percent error for hisprediction?
To find the percent error
percent error = | (actual - expected)/ actual| * 100 %
The actual is 40 and the expected is 42
percent error = | ( 40 - 42) / 40 | * 100 %
= | -2/40| * 100%
= .05 * 100 %
= 5%
find the percent notation 7/10
A notation is a way of communicating through symbols or signs, or it might be a brief written message. A chemist notating AuBr for gold bromide is an illustration of a notation. A quick list of things to accomplish is an illustration of a notation.
Explain about the percent notation?Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The sign "%" is used to denote it.
When expressing a fraction as a percentage, we multiply the provided fraction by 100.7/10, which is 70%.
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The marching band director is standing on a platformoverlooking the band practice. The pit section is located 8feet from the base of the platform. If the angle ofdepression from the band director to the pit section is 67°find the height of the platform.
Through trigonometry, we calculated that the height of the platform is 18.8 feet.
The director of the marching band is observing the band practice from a platform. 8 feet separate the base of the platform from the pit area. If the pit section's angle of depression is 67 degrees from the band director,
The angle formed by the horizontal line and the item as seen from the horizontal line is known as the angle of depression. When the angles and the separation of an object from the ground are known, it is mostly used to calculate the distance between the two objects.
We have,
So, the Angle of Depression = [tex]\alpha[/tex] = 67
Let x be the height of the platform,
Tan [tex]\alpha = \frac{x}{8}[/tex]
[tex]Tan 67 = \frac{x}{8} \\\\2.35 =\frac{x}{8} \\x = 2.35 *8 = 18.8[/tex]
Hence, The height of the platform is 18.8 feet.
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A tree casts you say shadow that is 9 feet long at the same time a person standing nearby casts a shadow that is 3 feet long if the person is five point feet tall how tall is the tree
we have that
Applying proportion
x/9=5.5/3
solve for x
x=9*(5.5/3)
x=16.5 ft
therefore
the answer is 16.5 ftRecoverySolve for x usingcross multiplication.2x + 132x11 -=x + 22x = [?]Enter
Answer:
x = 4
Step-by-step explanation:
Cross-multiplying means multiplying the numerator of one side by the denominator of the other side.
So, let's multiply the sides:
[tex]\begin{gathered} \frac{2x+1}{3}=\frac{x+2}{2} \\ 2\cdot(2x+1)=3\cdot(x+2) \end{gathered}[/tex]Now, we can solve each side:
[tex]\begin{gathered} 4x+2=3x+6 \\ 4x-3x=6-2 \\ 1x=4 \\ x=4 \end{gathered}[/tex]So, x = 4.
Write the following numbers in decreasing order: −4; 1 2/3 ; 0.5; −1 3/4 ; 0.03; −1; 1; 0; -103; 54
Decreasing order means from largest to smallest
The ordered list is:
54, 1 2/3, 1, 0.5, 0.03, 0, -1, -1 3/4, -4, -103
what is the value of the q that makes the equation true? 3(q+4)-10q=2q+3
Find x when the f(x) = 350 - 125x ; when f(x) = 0.
ANSWER
x = 2.8
EXPLANATION
The function given is:
f(x) = 350 - 125x
We want to find the value of x when f(x) = 0.
This means that:
[tex]\begin{gathered} f(x)\text{ = 350 - 125x} \\ \Rightarrow\text{ 0 = 350 - 125x} \\ \Rightarrow\text{ 125x = 350} \\ \frac{125x}{125}\text{ = }\frac{350}{125} \\ x\text{ = 2.8} \end{gathered}[/tex]That is the value of x