It is a mixed number:
[tex]5\frac{7}{10}[/tex]THe whole part, 5, is going to stay 5.
Now, let's work with the fractional part.
7/10 into a decimal would require for division.
7 divided by 10 is 0.7
Thus,
IN Decimal, it will be "5.7"
To find percentage from decimal, we multiply by 100 and tag along a % sign.
So,
[tex]5.7\cdot100=570[/tex]The number, in percentage, is 570%
Caitlin and her family eat at at a restaurant. They spend $240 before tax. The restaurant charges them an additional 8% tax on their bill. Complete the two expressions that represent the total cost of the bill after the 8% tax is added to the bill. 240+ _______ x240240+_______Which 2 of these go in the blank?A.) 8B.) 0.08C.) 0.80D.) 19.20E.) 192F.) 259.20G.) 24
Answer:
B.) 0.08
D.) 19.20
Explanation:
The cost of the meal before tax = $240
Percentage added as tax = 8%
Therefore, the total cost of the bill after the 8% tax is added to the bill is:
[tex]\begin{gathered} 240+8\%\times240 \\ =240+\frac{8}{100}\times240 \\ =240+0.08\times240 \end{gathered}[/tex]If we simplify further, we have:
[tex]=240+19.20[/tex]The sum of 3 and r is less than 7.What number sentence represents the statement?
The sum of 3 and r can be represented by "3 + r"
If this sum is less than 7, we can use the symbol "lesser than" (<) to compare the sum with the number 7, so our number sentence is:
[tex]3+r<7[/tex]There are no solutions to the system of inequalities shown below. y< 4X-6 y > 4x + 2 A.true B. false
The graphs of both inequalities is shown below;
Please note that the red region with the broken lines represents y < 4x - 6
The blue blue region with the broken lines represent y > 4x + 2
Observe carefully that both graphs run parallel to each other and there is no point of intersection. This means there is no values of x and y that can satisfy both inequalities.
Simply put, there are no solutions to the system of inequalities shown.
The answer is
A: TRUE
two systems of equations are given below. for each system, choose the best description of its solution. if applicable, give the solution.
Let:
[tex]\begin{gathered} x-4y=8_{\text{ }}(1) \\ -x-4y=8_{\text{ }}(2) \\ \end{gathered}[/tex]Using elimination method:
[tex]\begin{gathered} (1)+(2) \\ x+(-x)+(-4y)+(-4y)=8+8 \\ -8y=16 \\ y=\frac{16}{-8} \\ y=-2 \end{gathered}[/tex]Replace the value of y into (1):
[tex]\begin{gathered} x-4(-2)=8 \\ x+8=8 \\ x=8-8 \\ x=0 \end{gathered}[/tex]The system has unique solution:
[tex](x,y)=(0,-2)[/tex]A cylinder sits on top of the rectangular prism. What is the combined volume? (use the Pi, round to the nearest tenth of an inch) ______ in3
The combined volume is:
[tex]V=V_{rp}+V_c[/tex]The volume of the rectangular prism is:
[tex]V_{rp}=l\cdot w\cdot h[/tex]The volume of a cylinder is:
[tex]V_c=\pi\cdot r^2\cdot h[/tex]Then, the combined volume is:
[tex]\begin{gathered} V=l_{rp}\cdot w_{rp}\cdot h_{rp}+\pi\cdot r^2\cdot h_c \\ \\ V=10m\cdot5m\cdot3m+\pi\cdot(2m)^2\cdot4m \\ V=150m^3+16\pi m^3 \\ V=(150+16\pi)m^3 \\ \\ V\approx200.3\text{ }m^3 \end{gathered}[/tex]Turn into inches:
[tex]200.3m^3\cdot\frac{61023.7in^3}{1m^3}=12223047in^3[/tex]Then, the volume in inches is 12,223,047 cubic inches (200.3 cubic meters)
Simplify (5x + 7) - (x + 2)
You have the following expression:
(5x + 7) - (x + 2)
in order to simplify the previous expression, eliminate parenthesis and take into account that if a parenthesis is preceeded by a minus sign, when you elminate th eparenthesis the sign inside change to the opposite, just as follow:
(5x + 7) - (x + 2) =
5x + 7 - x - 2 =
5x - x + 7 - 2 =
4x + 5
Hence, the simplified expression is 4x + 5
10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.
SOLUTION
A.
To solve this question, we will use the compound interest formula.
Which is:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]The continuous decay rate is 0.771%
B.
Using the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]The population of the city in the year 2021 is 97,972.
C.
We will use the same formula:
[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]List all real values of x such that f(x) = 0, if there are no such real x, type DNE in the answer blank. If there is more than one real x, give a comma separated list (i.e: 1, 2) X =
Given the function defined as:
[tex]\begin{gathered} f(x)=-7+\frac{-8}{x-6} \\ \end{gathered}[/tex]The function can further be expressed as:
[tex]f(x)=-7-\frac{8}{x-6}[/tex]Find the LCM of the function;
[tex]\begin{gathered} f(x)=\frac{-7(x-6)-8}{x-6} \\ f(x)=\frac{-7x+42-8}{x-6} \\ f(x)=\frac{-7x+34}{x-6} \\ \end{gathered}[/tex]If f(x) = 0, then the value of x is calculated as:
[tex]\begin{gathered} \frac{-7x+34}{x-6}=0 \\ -7x+34=0 \\ -7x=0-34 \\ -7x=-34 \end{gathered}[/tex]Divide both sides of the equation by -7:
[tex]\begin{gathered} \frac{\cancel{-7}x}{\cancel{-7}}=\frac{\cancel{-}34}{\cancel{\square}7} \\ x=\frac{34}{7} \end{gathered}[/tex]Therefore the value of x if f(x) = 0 is 34/7
Use the graph to find the horizontal asymptote of the rational function
Horizontal Asymptote
Observing the graph with the red dashed line, the horizontal asymptote of the function is at y = 6
Vertical asymptote
If we draw a line the graph we have the following
This indicates that the vertical asymptote is at x = 2.
if you halved a recipe that calls for 5 c. chicken broth how much broth would you use
If halved a recipe that calls for 5 c chicken broth, then you would end up using 2.5 c chicken broth (that is two and half c of chicken broth).
I need to know The answer to this word problem
Given:
The little cheese 8 in $ 7.
The big cheese 10 in $ 9.
The cheese monster 12 in $ 12.
Required:
To find the ratio of little cheese, big cheese and cheese monster.
Explanation:
(1)
The crust to prize ratio for little cheese is,
[tex]\begin{gathered} 8:7=1:? \\ \\ =\frac{7}{8} \\ \\ =0.875 \end{gathered}[/tex](2)
The crust to prize ratio for big cheese is,
[tex]\begin{gathered} 10:9=1:? \\ \\ =\frac{9}{10} \\ \\ =0.9 \end{gathered}[/tex](3)
The crust to prize ratio for cheese monster cheese is,
[tex]\begin{gathered} 12:12=1:? \\ \\ =\frac{12}{12} \\ \\ =1 \end{gathered}[/tex](4)
The cheese monster is the best pizza for him.
Final Answer:
The crust to prize ratio for little cheese is = 0.875
The crust to prize ratio for big cheese is = 0.9
The crust to prize ratio for cheese monster cheese is = 1
The cheese monster is the best pizza for him.
8. In order to reach the top of a hill which is 250 feet high, one must travel 2000 feet straight up a road
which leads to the top. Find the number of degrees contained in the angle which the road makes with the
horizontal.
7.18° the angle which the road makes with the horizontal.
Define Trigonometric functions
The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Given,
Height of hill = 250 feet
Length of the slope = 2000 feet
find the angle,
we know, sin(x) = perpendicular / hypotenuse
sin(x) = 250 / 2000
x = sin^-1 (0.125)
x = 7.18°
Hence, 7.18° the angle which the road makes with the horizontal.
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Solve each word problem using a system of equations. Use substitution or elimination. 1. One number added to three times another number is 24. Five times the first number added to three times the other number is 36.
ANSWER
The first number is 3 and the second number is 7
EXPLANATION
Let the first number be x.
Let the second number be y.
The first line of the word problem is:
One number added to three times another number is 24.
This means that:
x + 3(y) = 24
=> x + 3y = 24 ______(1)
The second line of the word problem is:
Five times the first number added to three times the other number is 36.
5(x) + 3(y) = 36
5x + 3y = 36 ______(2)
Now, we have a system of equations:
x + 3y = 24 ____(1)
5x + 3y = 36 ___(2)
From the first equation, we have that:
x = 24 - 3y
Substitute that into the second equation:
5(24 - 3y) + 3y = 36
120 - 15y + 3y = 36
Collect like terms:
-15y + 3y = 36 - 120
-12y = -84
Divide through by -12:
y = -84 / -12
y = 7
Recall that:
x = 24 - 3y
=> x = 24 - 3(7) = 24 - 21
x = 3
Therefore, the first number is 3 and the second number is 7.
question In photograph
The equation that represents the relationship between x and y in the table is (L.) y = -5x + 3.
What is an Equation in Math?In mathematics, an equation is a relationship between two expressions that are expressed as equality on each side of the equal to sign.
Given in the table is the relationship between x and y respectively.
Substitute the values of x in the respective equations to find the value of y, the resulting value which matches the value of y in the table determines the correct equation.
J. y = -5x -27
⇒ For x = -3, y = -5(-3) - 27 = 15 -27 = -12 ≠ 18
K. y = -5x + 18
⇒ For x = -3, y = -5(-3) + 18 = 15 + 18 = 33 ≠ 18
L. y = -5x + 3
⇒ For x = -3, y = -5(-3) + 3 = 15 + 3 = 18 ≈ 18
For x = -1, y = -5(-1) + 3 = 5 + 3 = 8
For x = 2, y = -5(2) + 3 = -10 + 3 = -7
For x = 6, y = -5(6) + 3 = -30 + 3 = -27
All the values of x and y in the table satisfy the equation y = -5x + 3. Hence this is the required equation that represents the relationship.
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N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3-
Solution
Given:
2x - 4y = -2
3x + 2y = 3
Substitution method
[tex]\begin{gathered} From\text{ 3x+2y=3} \\ 3x=3-2y \\ x=\frac{3-2y}{3} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ }x=\frac{3-2y}{3}\text{ into the first equation} \\ 2x-4y=-2 \\ 2(\frac{3-2y}{3})-4y=-2 \\ \frac{6-4y}{3}-4y=-2 \\ Multiply\text{ }trough\text{ by 3} \\ 6-4y-12y=-6 \\ 6-16y=-6 \\ -16y=-6-6 \\ -16y=-12 \\ y=\frac{-12}{-16} \\ y=\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} Substitute\text{ y=}\frac{3}{4}\text{ into }x=\frac{3-2y}{3} \\ x=\frac{3-2(\frac{3}{4})}{3}=\frac{3-\frac{3}{2}}{3}=\frac{\frac{6-3}{2}}{3}=\frac{\frac{3}{2}}{3} \\ x=\frac{3}{6} \\ x=\frac{1}{2} \end{gathered}[/tex][tex]Thus,\text{ x=}\frac{1}{2},y=\frac{3}{4}[/tex]Graphical method:
Plot the graph of the two equations on the same graph
The point of intersection of the two graphs gives the solution to the system of equations
The point of intersection is (0.5, 0.75)
Which in fraction gives (1/2, 3/4)
Thus. x = 1/2, y= 3/4
a is less than or equal to 10
The expression of the mathematical statement is a ≤ 10
How to represent the mathematical statement as an expression?From the question, we have the following mathematical statement that can be used in our computation:
a is less than or equal to 10
The key statement less than or equal to in mathematics and algebra can be represented using the following symbol
less than or equal to ⇒ ≤
So, we have the following representation
a is less than or equal to 10 ⇒ a is ≤ 10
This implies that we rewrite the above expression as follows
So, we have
a is less than or equal to 10 ⇒ a ≤ 10
The above expression cannot be further simplified
So, we leave it like that
Hence, the mathematical statement when expressed as an expression is a ≤ 10
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Graph the line with the given slope m and y-intercept b.
m = 1, b =0
Answer:
See graph
Step-by-step explanation:
write the equation of the polynomial with the following zeros in standard form
Answer:
x² - (5 + √7)x + 5√7
Explanation:
A polynomial with zeros at x = a and x = b can be written as:
(x - a)(x - b)
So, if the roots are x = √7 and x = 5, we can write the equation for the polynomial as follows:
(x - √7)(x - 5)
Then, to write it in standard form, we need to apply the distributive property, so:
[tex]\begin{gathered} (x-\sqrt[]{7})(x-5)=x\cdot x+x(-5)-\sqrt[]{7}x-\sqrt[]{7}(-5) \\ (x-\sqrt[]{7})(x-5)=x^2-5x-\sqrt[]{7}x+5\sqrt[]{7} \\ (x-\sqrt[]{7})(x-5)=x^2-(5+\sqrt[]{7})_{}x+5\sqrt[]{7} \end{gathered}[/tex]Therefore, the answer is:
x² - (5 + √7)x + 5√7
simplifying with like terms; 2(m+10)
In order to simplify the expression, we would multiply the terms inside the bracket by the term outside. It becomes
2 * m + 2 * 10
= 2m + 20
sorry its blurry[tex] \frac{3x - 2}{4} = 2x - 8[/tex]
the given expression is,
[tex]\frac{3x-2}{4}=2x-8[/tex][tex]\begin{gathered} 3x-2=4(2x-8) \\ 3x-2=8x-32 \\ 8x-3x=32-2 \end{gathered}[/tex][tex]\begin{gathered} 5x=30 \\ x=\frac{30}{5} \\ x=6 \end{gathered}[/tex]thus, the answer is x = 6
i am stuck and need help ASAP with itfind the area
Given:
Required:
We want to find the area of given
Explanation:
As we can see that measurement of given figure is 5 by 5 so it is square and the area of square is
[tex]5*5=25\text{ unit}^2[/tex]Final answer:
25 sq unit
what are the two moves you can use to get the first figure to the second figure (dilation,rotation, reflection,and translation)
ANSWER:
Dilation and translation
EXPLANATION:
Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.
The figure was translated 6 units right and 7 units down.
The translation rule that occured here is==> (x+6, y-7)
Also, a dilation with a scale factor of 2 occured here.
Therefore, a dilation and translation occured in order to get the first figure to the second figure.
4. The relationship between temperature expressed in degrees Fahrenheit(F) and degrees Celsius (C) is given by the formula F= (9/5)C + 32. If the temperature is 5 degrees Fahrenheit, what is it in degrees Celsius ?
To calculate which value in Celsius the temperature of 5 Fº equates to, we first need to rewrite the expression isolating the "C" variable on the left side.
[tex]\begin{gathered} F=\frac{9}{5}\cdot C+32 \\ \frac{9}{5}\cdot C=F-32 \\ 9\cdot C=5\cdot F-160 \\ C=\frac{5}{9}\cdot F-\frac{160}{9} \\ \end{gathered}[/tex]We now need to replace F by 5.
[tex]\begin{gathered} C=\frac{5}{9}\cdot5-\frac{160}{9} \\ C=\frac{25}{9}-\frac{160}{9} \\ C=\frac{-135}{9} \\ C=-15 \end{gathered}[/tex]The temperature is -15 degrees in Celsius.
6. Express the given function h as a composition of two functions f and g
such that H(x) = (fog)(x).
a) H(x) = |3x +2|
b) H(x) = √√√√5x +4
The given function can be represented f(x) and g(x) as below
What are functions?
A function from X to Y is an assign of each constituent of Y to each variable of X. The set X is known as the function's scope, while the set Y is known as the function's image domain. The notation f: XY denotes a function, its domain, and its codomain, and the value of a function f at an element x of X, indicated by f(x), is known as the image of x under f, or the value of f applied to the argument x. When defining a function, the domains and codomain are not often explicitly specified, and without performing some (complicated) calculation, one may only know that perhaps the domain is included in a larger package.
The functions are
(a) f(x) = 3x+2 and g(x) = |x|
so, H(x) = f(g(x)) = |3x+2|
(b) f(x) = 5x+4 and g(x) = √√√√x
so, H(x) = f(g(x)) = √√√√5x+4
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help meeeeeeeeee pleaseee !!!!!
For the two given functions, the compositions are:
(f o g)(x) = √(2x + 3)(g o f)(x) = 2*√x + 3How to find the two compositions?
Here we have two functions:
f(x) = √x
g(x) = 2x + 3
Now we want to get the compositions:
(f o g)(x) = f( g(x))
So here we just need to evaluate f(x) in g(x), we will get:
(f o g)(x) = √g(x) = √(2x + 3)
The other composition is:
(g o f)(x) = g(f(x)) = 2*f(x) + 3 = 2*√x + 3
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Two methods to solve (X+3)^2=6
The solution of the given equation is [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Given equation:-
[tex](x+3)^2=6[/tex]
We have to find the value of x by solving the given equation.
We can rewrite the given equation as:-
[tex]x^2+6x+9=6\\x^2+6x+3=0[/tex]
We can solve the the quadratic equation by finding the discriminant.
[tex]x = \frac{-6+-\sqrt{6^2-4*1*3} }{2*1}[/tex]
[tex]x = \frac{-6+-\sqrt{36-12} }{2}[/tex]
[tex]x=\frac{-6+-2\sqrt{6} }{2}=-3+-\sqrt{6}[/tex]
Hence, the values of x are [tex]-3+\sqrt{6}[/tex] and [tex]-3-\sqrt{6}[/tex].
Discriminant
In arithmetic, a polynomial's discriminant is a function of the polynomial's coefficients.
Quadratic equation
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
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BUSINESS MATH calculate the state income tax owed on a 50,000 per year salary
Hello there. To solve this question, we have to remember some properties about income and taxes.
The following table shows the progressive tax rate for calculating individual income tax:
We want to calculate the state income tax owed on a $50,000 per year salary.
For this, notice this value is contained in the interval 17,001 and up, hence the progressive tax rate for this value is 5.75%.
In this case, the tax is simply given by the product between the value and the rate:
Don't forget to divide the percentage value by 100% before multiplying.
[tex]50000\cdot\dfrac{5.75}{100}=\$2,875[/tex]This is the state income tax owed by one whose salary is $50,000 per year.
Identify the postulate illustrated by the statement: Line ST connects pointS and point T
We have two points known to be ( S ) and ( T ). A line connects two points.
The minimum number of points that are required to form a straight line in a cartesian coordinate system are ( two ).
The minimum number of points that are required to form a plane in a cartesian coordinate system are ( three ) which will form two vectors i.e it requires two lines formed with a common point.
Two planes always intersect at exactly one point with direction normal to the two plane normal vectors.
Hence, the only possible postulate that relates two points is the formation of a line between two points; hence, the correct postulate for the given statement is:
[tex]\text{\textcolor{#FF7968}{Through any two points there is exactly one line}}[/tex]
May I please get help with this math problem. I have been trying many times to find all correct answers to each length.
To draw a triangle, you cannot take three random line segments, they have to satisfy the triangle inequality theorems.
0. Triangle Inequality Theorem One: the lengths of any two sides of a triangle must add up to more than the length of the third side.
Procedure:
• Evaluating the first values given: (adding the two smallest values)
[tex]5.2+8.2=13.4[/tex]Now, we have to compare this addition with the bigger value. As 13.4 > 12.8, these can be side lengths of a triangle.
• Evaluating the second values given: (adding the two smallest values)
[tex]5+1=6[/tex]Comparing this addition with the bigger value, we can see that 6 < 10, meaning that these values cannot be side lengths of a triangle.
• Evaluating the third values given: (adding the two smallest values)
[tex]3+3=6[/tex]Comparing, we can see that 6 < 15. Therefore, these cannot be side lengths of a triangle.
• Evaluating the final values given:
[tex]7+5=12[/tex]We can see that 12 < 13, so these cannot be side lengths of a triangle.
Answer:
• 12.8, 5.2, 8.2: ,can be side lengths of a triangle.
,• 5, 10, 1: ,cannot be side lengths of a triangle.
,• 3, 3, 15: ,cannot be side lengths of a triangle.
,• 7, 13, 5: ,cannot be side lengths of a triangle.
I need help I am doing 8th grade conversion factors and there is only one way my teacher wants me to do it.
Conversion factors are the numbers for which we need to multiply a certain variable to convert it to another unit. In this case we need to convert gallons to cups, which have a conversion factor of 16 and minutes to seconds, which has a conversion rate of 60. Doing this we have:
[tex]\text{capacity = 24 gallons }\cdot\text{ 16 = }384\text{ cups}[/tex][tex]\text{time = 5 minutes }\cdot\text{ 60 = }300\text{ s}[/tex]The rate is:
[tex]\text{rate = }\frac{384}{300}\text{ = }1.28\text{ }\frac{cups}{s}[/tex]