Alicia has at most $196 this means that her amount of money is less or equal than $196, we can express this as an inequality, like this:
[tex]\text{y}\leq\text{ \$}196-x[/tex]Where x represents the cost associated with the hat and the gloves and y is the money that left after the purchase of these articles
b = (2a)²
Work out the value of b when a = 5
Answer:
100
Step-by-step explanation:
in an election, suppose that 55% of the voters in fact support funding the new crc library building. a news organization wants to predict the outcome of the election by sampling 80 voters. what is the probability that less than 49% of the sampled voters support the new crc library building? this would result in the news organization making a wrong prediciton.
The new organization making a wrong prediction cannot be determined.
Probability is the branch of discrete mathematics. It is used for calculating how likely an event is to occur or happen.
According to the problem,
p = 55% ≅ 0.55
n = 80 voters
The probability that less than 49% ≅ 0.49 of the sampled voters support the new library building can be calculated as,
p( p < 0.49 ) = p( z < (0.49 - 0.55) / √(0.55*(1 - 0.55)/80) )
where, z = { p - p/ √(p(1 - p)/n) }
p( p < 0.49 ) = p( z < ( -0.06) / √(0.55*0.45/80))
= p( z < ( -0.06) / √(0.2475/80))
= p( z < ( -0.06) / [tex]\sqrt{0.00309375}[/tex] )
= p( z < ( -0.06) / 0.055621488 )
= p( z < ( -1.078719793) )
p( p < 0.49 ) = p( z < ( -1.079) )
p( p < 0.49 ) ≅ 0.140071 ( From the normal standard table )
The calculated probability is unpredictable. Therefore, We cannot say that the new organization is making a wrong prediction.
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Find the value of 3a + 2b if a = 4 and b = (-9) (*Substitute*)
Question:
Find the value of 3a + 2b if a = 4 and b = (-9) .
Solution:
Let the following expression
[tex]3a\text{ + 2b}[/tex]now, if a = 4 and b = -9, and we substitute them in the previous expression, we obtain:
[tex]3(4)\text{ + 2(-9) = 12 - 18 = -6}[/tex]then, we can conclude that the correct answer is:
[tex]-6[/tex]m∠1 =?
m∠2 = ?
m∠3 = ?
Answer:
1= 31 degrees
2= 121 degrees
3= 47 degrees
Step-by-step explanation:
IMPORTANT: SUM OF ALL THREE ANGLES OF A TRIANGLE EQUAL 180
For angle 1 we add 59+90 since those are the 2 known angles
90+59=149
Now subtract by 180
180-149=31
Angle 1 is equal to 31
Now for angle 2 we subtract 59 from 180 since it is on a flat surface the sum of those angles will equal 180 degrees
180-59=121
Angle 2 is 121 degrees
Now for angle 3 we add 121 and 12 since we know those 2 angles
121+12=133
Now subtract from 180
180-133= 47
Angles 3 is 47 degrees
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Solve right triangle ABC for all missing parts. Express angles in decimal degrees.a = 200.7 km, c= 401.5 kmRound to the nearest hundred
Using the Pythagorean Theorem we get:
[tex]c^2=a^2+b^2\text{.}[/tex]Therefore:
[tex]b^2=c^2-a^2\text{.}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]b^2=(401.5km)^2-(200.7km)^2.[/tex]Solving the above equation for b we get:
[tex]\begin{gathered} b=\sqrt[]{(401.5km)^2-(200.7km)^2} \\ =\sqrt[]{161202.25km^2-40280.79km^2} \\ =\sqrt[]{120921.76km^2}\approx347.74km\text{.} \end{gathered}[/tex]Now, from the given diagram we get that:
[tex]\begin{gathered} \cos B=\frac{a}{c}, \\ \sin A=\frac{a}{c}\text{.} \end{gathered}[/tex]Substituting a=200.7km and c=401.5km we get:
[tex]\begin{gathered} \cos B=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \\ \sin A=\frac{200.7\operatorname{km}}{401.5\operatorname{km}}=\frac{2007}{4015}\text{.} \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} B=\cos ^{-1}(\frac{2007}{4015})\approx60.00^{\circ}, \\ A=\sin ^{-1}(\frac{2007}{4015})\approx30.00^{\circ}, \end{gathered}[/tex]Answer:
[tex]\begin{gathered} b=347.74\operatorname{km}, \\ B=60.00^{\circ}, \\ A=30.00^{\circ} \end{gathered}[/tex]
5. Complete the table to fill in the points that satisfy the equation: y = 1/3 x + 5?
Answer:
Step-by-step explanation: For this question, we need to make a table first.
For which we'll assume values of x and y.
Let the value of x be 0 then y will be 5
if value of x=3 then y=6
hence, we arrive at two points that are satisfying the equation.
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graph the circle which is centered at (-5,1) and which has a point (-2,-3) on it
We can start by placing the center at (-5,1).
The radius of the circle will be the distance between the center and the point (-2,-3).
If we graph this two points, we can use an angle protractor to draw the circle passing through point P(-2,-3) and centered at (C(-5,1):
Which relationship between x and y in the equation shows a proportional relationship? o y=+3 o y y= 12 O y = 2x + 6 o y = 12x
Maria used a number line to find 12 ÷ 4.
Explain how she can use the number line to model the division.
Maria can draw a number line connecting the points 0 and 12, then divide the distance between them into four equal parts. The division operation produces the location of the point closest to zero.
What is number line ?A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in elementary mathematics. Every point on a number line is assumed to be a real number, and every real number is assumed to be a point.
Integers are frequently represented as specially marked points evenly spaced on a line. Despite the fact that the image only shows the integers from -3 to 3, the line includes all real numbers, which continue indefinitely in each direction, as well as numbers that are between the integers. It is frequently used to help teach simple addition and subtraction, particularly with negative numbers.
The number line is also known as a real line or real number line in advanced mathematics. It is formally defined as the set R of all real numbers viewed as a geometric space, namely the Euclidean space of dimension one. It's also known as a vector space, metric space, topological space, measure space, or linear continuum.
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On the radio one morning, a weather reporter stated that the temperature was two degrees below zero, but the temperature would continue to rise throughout the day. Which inequality could be used to represent all the temperature readings, T, that day?
the inequality for this situation is
T >= -2
[tex]T\ge-2[/tex]The scale along each als is 1.State the interval where f (2)
We have the following:
replacing:
[tex]\begin{gathered} f(2)The answer is the interval (-6, 9)Kelly opened a simple interest account with deposit of $2200. At the end of 4 years, the balance of the account was $2200. What is the annual interest rate on the account.
The simple interest formula is:
I = P R T, where I is the interest earned, P is the principal, R is the insterst per year and T is the time in years
If the initial deposit is $2,200 and after 4 years the balance is still $2,200, then the interest rate is zero
An amusement park charges $35.50 for admission. On Saturday 6789 people visited the park. About how much money did the park earn from admission that day?
ESTIMATE PLEASE!!
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
we have
Write a quadratic equation in standard form whose graph passes through the given points (1,2) (2,-1) (3,-6)
A quadratic equation in standard form is equal to
y=Ax^2+Bx+C
substitute the given values
(1,2)
2=A(1^2)+B(1)+C
2=A+B+C ------> equation 1
(2,-1)
-1=A(2^2)+B(2)+C
-1=4A+2B+C -------> equation 2
(3,-6)
-6=A(3^2)+B(3)+C
-6=9A+3B+C -------> equation 3
step 1
In the equation 1 isolate the variable A
A=2-B-C -------> equation 4
step 2
substitute equation 4 in equation 2 and 3
-1=4(2-B-C)+2B+C
-1=8-4B-4C+2B+C
-1=8-2B-3C
2B+3C=
Raymond invested $4, 000 in a new company. The value of his investment has been growing at a rate of 6% per year for the last 5 vears. Write a function to represent the growth of his investment of $4,000, where A is the total value of his investment and t is the time invested in years. What is the total value of his investment after 5 years?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{per year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 5} \implies A=4000(1.06)^5\implies A \approx 5352.90[/tex]
now, we're assuming is a 6% growth of the current amount per year, namely compounded, as opposed to simple interest.
solve for X using cross multiplication 4x-3/3 = x+8/2 x= []
Answer:
x=6
Explanation:
Given the equation:
[tex]\frac{4x-3}{3}=\frac{x+8}{2}[/tex]First, cross multiply:
[tex]2(4x-3)=3(x+8)[/tex]Next, open the brackets:
[tex]8x-6=3x+24[/tex]Subtract 3x from both sides of the equation:
[tex]\begin{gathered} 8x-3x-6=3x-3x+24 \\ 5x-6=24 \end{gathered}[/tex]Add 6 to both sides of the equation:
[tex]\begin{gathered} 5x-6+6=24+6 \\ 5x=30 \end{gathered}[/tex]Finally, divide both sides by 5:
[tex]\begin{gathered} \frac{5x}{5}=\frac{30}{5} \\ x=\frac{6\times5}{5} \\ x=6 \end{gathered}[/tex]The value of x is 6.
The curve above is the graph of a sinusoidal function. It goes through the points (- 4, 0) and (2, 0) Find a sinusoidal function that matches the given graph If needed, you can enter pi = 3.1416 as in your answer, otherwise use at least 3 decimal digits
A sinusoidal function that matches the given graph is y=cosπx/3+2.
From the given question, the curve is the graph of a sinusoidal function.
It goes through the points (- 4, 0) and (2, 0).
We have to find the sinusoidal function that matches the given graph.
For this problem, we can use either of these general equations :
y = Asin(Bx + C) + D or y = Acos(Bx + C) + D.
A = amplitude = distance on Y-axis from centre of graph to highest or lowest point.
So from the given graph
A = 1
T = period = distance on X-axis over one complete cycle
So from the given graph
T = 6.
So B=2π/6 =π/3
D = distance that graph has been moved up or down on the Y-axis
D = 0
C= horizontal shift (left side if positive)
From the given Graph
C = 2
So, equtaion is
y = Acos(Bx + C) + D
Putting the each variable value
Using π =3.1416.
y = 1*cos(π/3 x + 2) + 0
y = cosπx/3 + 2
Hence, a sinusoidal function that matches the given graph is y=cosπx/3+2.
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write an equation in slope intercept form for the line with the slope 1/5 and y - intercept 6
Given data:
The given slope of the line is m=1/5 .
The given y-intercept is c=6.
The expression for the equation of the line in slope intercept form is,
[tex]y=mx+c[/tex]Subbstitute the given values in the above expression.
[tex]y=\frac{1}{5}x+6[/tex]Thus, the equation of the line in slope intercept form is y=(1/5)x+6.
A heptagon has angles measure of 105°, 141°, 132°, 109°, 143° and 131°. What is the measure of the seventh angle?
A fruit juice owner has three types of juices. 320 liters of the first kind, 350 liters of the second kind, 400 liters of the third kind. How many bags with the amount of each juice will he be able to do?
Three types of juice means 3!
that is ., 3*2*1 =6
He will be able to fill 6 bags with the specified amount of each juice.
In mathematics, the term "factorial" refers to the sum of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.
What is a factorial problem?In a factorial, you multiply the supplied integer by all of the positive whole numbers that are less than it. To put it another way, = n (n 1) ... 2 1.The mathematical operation known as a factorial, denoted by the symbol (! ), multiplies a number (n) by each number that comes before it. The factorial function instructs you to multiply all the whole numbers starting at the selected number and going all the way down to one. In further mathematical terms, a number's factorial (n!) equals n (n-1).When a group of variables are independent happenings, a factorial distribution occurs. In other words, there is no interaction between the variables; for two events, x and y, the probability of x remains constant when y is taken into account. Therefore,To learn more about factorial refer to:
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Braelyn is writing an equation to represent the perimeter of a rectangle with the width equal to half the length. she knows that the perimeter is equal to 18 units and needs to find the length and width of the rectangle. which equations represent this relationship? select the four correct answers. x one-half x = 18 2 x x = 18 2 (x) 2 (2 x) = 18 x one-half x x one-half x = 18 2 (x one-half x) = 18 2 x one-half x = 18
The correct options are 2,3,4,5, according to given question.
What do you mean by equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
According to data in the given question,
We have the given information:
P = 18
w= l/2
Perimeter of a rectangle equals to twice the sum of length and width:
P= 2(l+w)
If we assume width = x, then:
l = 2x
2(x+2x) = 18 or
2x + 4x = 18
If we assume length = x, then:
w = 1/2x
2(x + 1/2x) = 18 or
2x + x = 18
Therefore, the correct options are below:
x + one-half x = 18 === incorrect
2 x + x = 18 === correct
2 (x) + 2 (2 x) = 18 === correct
x + one-half x + x + one-half x = 18 === correct, same as second option
2 (x + one-half x) = 18 === correct, same as second option
2 x + one-half x = 18 === incorrect
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Robert is standing on a bridge that spans a canyon. He drops a pebble from the bridge, and records how long the pebble takes to reach the water below. If the pebble takes 5.49 seconds to reach the water, what is the height of the bridge?
"Height of the bridge is 148 m"
Given :
time = 5.49 s
Since pebble is dropped from a height it will have acceleration due to gravity (g = 9.8 m/s²) ∴ a = 9.8 m/s²
Let us assume that Initial velocity (v) is 0 m/s² (pebble is not moving)
we have to find distance d = ?
Now according to formula
d = vt + 1/2 at²
Now putting the values in the formula
d = 0 × 5.49 + 1/2 × 9.8 × (5.49)²
d = 0 + 147.68
d = 147.68 ≈ 148 m
Therefore the height of the bridge is 148 m.
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help meeeeeeeeeeeeeee pleaseeeeeee help meeeeeeeeeeeeeee pleaseeeeeee
Answer:
Width = 4.7 m, Length = 6.7 m
Step-by-step explanation:
Let the width be [tex]w[/tex]. Then, the length is [tex]w+2[/tex].
[tex]w(w+2)=32 \\ \\ w^2+2w-32=0 \\ \\ w=\frac{-2 \pm \sqrt{2^2-4(1)(-32)}}{2(1)} \\ \\ w \approx 4.7 (w>0) \\ \\ w+2 \approx 6.7[/tex]
What is the answer for this equation 3X+y=5
The equation
[tex]3x+y=5[/tex]has two variables: x and y.
And since we have only one equation, the variables have infinite possible values, which are related to that equation.
Another way of seeing that is by calling x the independent variable, and then y will be the dependent variable (its value depends on the value of x).
So, we can isolate y on the left side of the equation, to obtain:
[tex]\begin{gathered} 3x+y=5 \\ \\ 3x+y-3x=5-3x \\ \\ y=-3x+5 \end{gathered}[/tex]Now, we see that the above equation represents a line (an infinite set of points), that has a slope -3 and a y-intercept 5.
Therefore, all the points on that line are solutions to the given equation.
If we graph that set of solutions on a xy-plane, we obtain the line below:
evaluate the expression (7-4)/(8÷2)
Start simplifying both numerator and denominator,
[tex]\begin{gathered} 7-4=3 \\ 8\div2=4 \end{gathered}[/tex]rewrite the expression
[tex]\frac{(7-4)}{8\div2}=\frac{3}{4}[/tex]The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer: 2 =
27⁰
111°
answer x=
The measure of angle of a triangle x is 42°.
According to the question,
We have the following information:
In a triangle, the measurements of two of its angles are 27° and 111°.
We know that the sum of three angles of a triangle is 180°.
So, we have the following expression to find the value of x:
27+111+x = 180
Adding the numbers on the left hand side:
(Note that the variable can not be added to any integer. It can only be added to the same variable.)
138+x = 180
Subtracting 138 from both the sides:
x = 180-138
x = 42°
Hence, the value of x for the given triangle is 42°.
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The table shows the temperature (v) at different altitudes (x). This is a linear relationship. Find the y-intercept for this relationship. 0 Altitude (ft), X Temperature (°F). 2,000 61 4,000 53 6,000 45 8,000 10,000 12,000 37 29 21 69 They-Intercept for this relationship is b =
PLEASE HELP ASAP!!! 30 POINTS IF YOU HEL ME!!! I WILL MARK BRAINLIEST!
Answer:
.
Step-by-step explanation:
Find the domain and function of the graph
The Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
Given that,
A graph of the function is shown, we have to determine the domain of the graph,
The domain is defined as the values of the independent variable for which there is a certain value of the dependent variable exists in the range of the function.
here,
The function is defined on the values of x, as 2, 6 and from 3 to 5,
So the domain of the function is said to be as 2, 6 and 3 ≤ x ≤ 5.
Thus, the Domain of the function is given as 2, 6 and 3 ≤ x ≤ 5.
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so I am doing Eureka math and 7th grade kinda need help....rewrite the expression by using distributive property and collecting like terms. 2 4/5v - 2/3(4v+1 1/6)
Answer:
2/15v + 7/9
Step-by-step explanation:
We take our base equation, then we will make every mixed number into an improper fraction. This will give us 14/5v - 2/3(4v+ 7/6). Then we will open the parentheses. This gives us: 14/5v - 8/3v+ 14/18. We will bring both the v's to a common denominator, giving us 42/15v - 40/15v+ 14/18. Then we can subtract and simplify. 2/15v + 7/9.