Table 1 shows two variables m and n that are related by an equation n ab^m where a and b are constantBelow shows table 1:m : 1 2 3 4 5n : 24 48 96 192 384a) plot the graph of log10 n against m by using a scale of 2 cm to 1 unit on the x-axis and 2cm to 1.2 unit on the y-axisb) hence, find the value of a and b
Answers
Answer
a) The plotted graph is shown in the Explanation below.
b) a = 12, b = 2
Explanation
n = a(b^m)
Taking the logarithm of both sides
log n = log [a(b^m)]
log n = log a + log (b^m)
log n = log a + m log b
So, to first plot the graph, we know we need to rewrite this equation to match the equation of a straight line. Equation of a straight line is
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
log n = (log b) m + log a
y = mx + b
y-axis = log n
slope = log b
x-axis = m
intercept = log a
So, we need to plot log n (on the y-axis) against m (on the x-axis)
m | n | log n
1 | 24 | 1.38
2 | 48 | 1.68
3 | 96 | 1.98
4 | 192 | 2.28
5 | 384 | 2.58
The values for log n are then plotted against the corresponding value of m
The image is presented below.
From the graph, we can easily see that
Intercept = 1
To obtain the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
Using the two farthest points,
(x₁, y₁) and (x₂, y₂) = (1, 1.38) and (5, 2.58)
[tex]\begin{gathered} Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ \text{Slope = }\frac{2.58-1.38}{5-1}=\frac{1.2}{4}=0.3 \end{gathered}[/tex]b) Intercept = log a = 1.08
a = log⁻¹ (1.08) = 12
Slope = log b = 0.3
b = log⁻¹ (0.3) = 1.995 = 2
n = 12 (2^m)
We can test this by putting values of m in the expression looking to get n
when m = 1,
n = 12 (2^1)
n = 12 (2) = 24
when m = 5
n = 12 (2^5)
n = 12 (32) = 384
So, our model works!!!
Hope this Helps!!!
Related Questions
Brainliest. Find x and length
Answers
Value of x is 4 and length of QR is 15cm.
Define parallelograms.A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal. The illustration displays a parallelogram ABCD with the coordinates AB II CD and AD II BC. Moreover, AB = CD and AD = BC. Non-Example: A parallelogram is not represented by a trapezium.
Given Data
In rectangle, two parallel line are equal.
PS = -1+ 4x
QR = 3x +3
So,
Value of x will be:
-1 + 4x = 3x +3
4x - 3x = 3 +1
x = 4
For length of QR,
3x +3
3(4) +3
12 +3
15
Value of x is 4 and length of QR is 15cm.
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A line passes through (5,-4) and (-1,-4). Write the equation of the line in slope-intercept form.
Answers
Explanation:
The formula of the slope of a line that passes through points (x1, y1) and (x2, y2) is:
[tex]m=\frac{y_1-y_2}{x_1-x_2}[/tex]For this problem the slope is:
[tex]m=\frac{-4-(-4)}{5-(-1)}=\frac{-4+4}{5+1}=\frac{0}{6}=0[/tex]A slope of zero indicates that the line is horizontal. Therefore it is a constant.
The slope-intercept form of the equation of a line is:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept. In this case, the slope is zero so we just have:
[tex]y=b[/tex]b is the y-coordinate of the given points: b = -4
Answer:
y = -4
y= -5x+2 (Function rule)
Answers
The complete table using function rule y = -5x+2 is:
x y
-2 12
0 2
2 -8
4 -18
What is a function rule for a table?A function table includes a function rule as well as input and output values. If we plug in various values for the input, we obtain corresponding values of output according to the function rule. The relationship between the input values x and the output values y always follows a pattern that is specified by the function rule.Given:
Function rule, y = -5x+2.
We have to find the values of y by substituting different values of x.
When,
x = -2
y = -5(-2) + 2 = 10+2 = 12
x = 0
y = -5(0) + 2 = 0+2 = 2
x = 2
y = -5(2) + 2 = -10+2 = -8
x = 4
y = -5(4) + 2 = -20+2 = -18
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Adrian's favorite hobby is to take underwater pictures of his favorite sea creatures. Adrian decides to dive 48 feet below sea level so he can take pictures of seahorses that are 55 feet below sea level. What is the total distance
between him and the seahorses?
Answers
The total distance between Adrian and the seahorses is 7 feet.
How to calculate distance between two planes below sea level?
Since, the values of distances of the planes from the sea level are given as reference, mere linear subtraction of the smaller value from the larger value will bring in the distance between the seahorses and Adrian constructively; if the value turns out to be negative for unforeseen reasons, the modulus of the value obtained will serve the purpose.
Given, the distance from sea level where seahorses dwell = d₁ = 55 feet
The distance from sea level Adrian would dive = d₂ = 48 feet
Distance between seahorses and Adrian = d₁ - d₂ = (55 - 48) feet = 7 feet
Thus, the total distance between Adrian and the seahorses is 7 feet.
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Explain the meaning of the point (1,2.5) In terms of the situation
Answers
Given
The recipe for the smoothie is made up of 5 cups of strawberries and 2 cups of bananas.
For the point (1,2.5)
It means that from the graph showing a plot of the numbers of cups, with the number of strawberries cups on the y-axis and the number of banana cups on the x-axis, the 2.5 is for the number of cups for strawberries while 1 is the number of cups of banana.
We can also say that
For every 1 cup of banana, there should be 2.5 cups of strawberries.
clasificar el siguiente polinomio2xy +9b -4z + 9
Answers
Los polinomios se clasifican según el número de términos que lo componen.
Los términos de una expresión están separados entre sí por los signos "+" y "-"
Se conoce como "monomio" a un polinomio con un solo término.
Son ejemplos de monomios:
6x²
2x
z
Un "binomio" es un polinomio de dos terminos.
Por ejemplo:
2x-3y
4x²+1
5y⁴z-2x²
Un "trinomio" es un polinomio con tres términos.
Por ejemplo:
2x+3y+z
y²-z+7
Un "cuadrimonio" es un polinomio de cuatro términos
Por ejemplo
xy+5y-9z+4
Los polinomios también pueden clasificarse según su grado. El grado del polinomio está dado por el valor del mayor exponente.
Un polinomio de grado cero es aquel que tiene coefficientes igual a cero.
Por ejemplo
0x²+0x
Un polinomio de primmer grado es aquel en el que la variable está elevada a la uno. En general este exponente no se escribe por lo que en un polinomio grado uno las variables no van a tener exponente.
Por ejemplo
x+2
x+y+4
Un polinomio de segundo grado es aquel cuyo mayor exponente es dos, es decir, tiene un termino elevado al cuadrado.
Por ejemplo:
x²
x+y²+3
x-9y+5z²-7
Un polinomio de tercer grado es aquel cuyo mayor exponente es tres, es decir, al menos una variable está elevada al cubo.
Por ejemplo:
x
x³+y²
2x-y³+25
Teniendo estas definiciones en cuenta, puedes clasificar el polinomio:
[tex]2xy+9b-4x+9[/tex]Este polinomio tiene 4 términos, "2xy", "9b", "4x" y "9" por lo que se lo puede clasificar como un cuadrimonio.
Como puedes ver, ninguna de las variables tiene exponente, es decir que, el exponente de mayor valor es 1, por lo que se puede clasificar como un polinomio de primer grado.
Entonces esta expresión es un cuadrimonio de primer grado
A six-sided number cube is rolled, and then a spinner with five equal sections labeled A through E is spun. What is the probability of rolling a number less than four and spinning a D?
Answers
Data:
• A six-sided number cube is rolled.
,• Then, a spinner with five equal sections labeled A through E is spun.
,• Probability of rolling a number less than four and spinning a D.
Procedure
To get the total probability, we have to get the probability for each situation.
• Six-sided number cube
As we have six sides, we have six numbers, then we can get the probability of rolling a number less than four, meaning rolling 3, 2 or 1, as follows:
[tex]P(x<4)=\frac{3}{6}=\frac{1}{2}[/tex]• Spinner with five equal sections
Similarly, we have five sides and we want to know the probability of getting a D:
[tex]P(x=D)=\frac{1}{5}[/tex]• Total probability
Finally, the total probability, as those are independent events, would be the multiplication of the probabilities:
[tex]P=\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}[/tex]Answer: 1/10
Answer:
1/10
Step-by-step explanation: I took the test
Find the value of w and YZ if Y is between X and Z
Answers
w = 4 and YZ=24
1) XY = 4w
YZ= 6w
XZ=12w-8
2) Let's draw this to better understand it
So using the Segment Addition Postulate principle, let's write and solve
12w-8 =4w+6w
12w-8=10w
12w-10w -8=10w-10w
2w-8=0
2w-8+8=8
2w=8
w=4
3) The value for YZ =
6w => 6(4) YZ =24
Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)
Answers
Given:
The expression is,
[tex]e^{6-8\ln (x)+\ln (y)}[/tex]Explanation:
Simplify the expression by using logathimic properties.
[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]Simplify further.
[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]So answer is,
[tex]\frac{e^6y}{x^8}[/tex]A recipe called for the ratio of sugar to flour to be 4:1 if you used 28 ounces of sugar how many ounces of flower would you need to use
Answers
Using ratios we can conclude that we need 7 ounces of flour.
What is the ratio?When the second number in the ordered pair, b, is not equal to 0, the ratio is written as a/b. An equation in which two ratios are made equal is known as a proportion. As an illustration, you could write the ratio as 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)A ratio in math displays how many times one number is contained in another. The ratio of oranges to lemons, for instance, is eight to six if there are eight oranges and six lemons in a bowl of fruit. The proportions of oranges to the total amount of fruit are 8:14 for oranges and 6:8 for lemons, respectively.So, ounces of flour need:
The ratio of sugar to flour is 4:1.The sugar used is 28 ounces.Then calculate for flour as follows:
4:1 = 28:x4/1 = 28/x4x = 28x = 28/4x = 7
Therefore, using ratios we can conclude that we need 7 ounces of flour.
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While visiting Yosemite National Forrest, Joe approximated the angle of elevation to the top of a hill to be 25 degrees. After walking 350 ft closer, he guessed that the angle of elevation had increased by 14 degrees. Approximately how tall is the hill?A. 475 feetB. 385 feetC. 608 feetD. 202 feet
Answers
The line sketch of the movement and positioning of Joe and the hill are shown below.
Brief description of the sketch made.
From the sketch, point A is where Joe started from heading towards the hill.
The hill is represented by BC and the height is h
25 degrees was the initial angle of elevation.
After moving 350 ft closer to the hill, the angle of elevation increased by 14 degrees to 25 + 14 = 39 degrees.
From triangle BCD,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 39=\frac{h}{x} \\ 0.8098=\frac{h}{x} \\ \text{Making h subject of the formula,} \\ h=0.8098x \end{gathered}[/tex]From triangle ABC,
Using the trigonometric function of tan,
[tex]\begin{gathered} \tan =\frac{opposite}{\text{adjacent}} \\ \tan 25=\frac{h}{350+x} \\ \text{Substituting the value of h gotten from the previous triangle,} \\ \tan 25=\frac{0.8098x}{350+x} \\ 0.4663=\frac{0.8098x}{350+x} \\ C\text{ ross multiplying,} \\ 0.4663(350+x)=0.8098x \\ 163.205+0.4663x=0.8098x \\ C\text{ ollecting the like terms,} \\ 163.205=0.8098x-0.4663x \\ 163.205=0.3435x \\ \text{Dividing both sides by 0.3435 to get x,} \\ x=\frac{163.205}{0.3435} \\ x=475.124ft \\ \\ \text{The height, h of the hill is;} \\ h=0.8098x \\ h=0.8098\times475.124 \\ h=384.755ft \\ h\approx385ft \end{gathered}[/tex]Therefore, the height of the hill is 385 feet
The correct answer is option B.
Solve the equation:2.5t=20
Answers
In order to solve this equation for t, we just need to divide both sides of the equation by 2.5.
So we have that:
[tex]\begin{gathered} 2.5t=20 \\ \frac{2.5t}{2.5}=\frac{20}{2.5} \\ t=\frac{20}{2.5} \\ t=8 \end{gathered}[/tex]So the solution for this equation is t = 8.
Find the equation (in terms of x ) of the line through the points (-2,4) and (1,-5)y=
Answers
To determine the equation of a line that passes through (x₁,y₁) you can use the following formula:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Substituting the given points in the above formula, you get:
[tex]y-4=\frac{4-(-5)}{-2-1}(x-(-2)).[/tex]Simplifying you get:
[tex]\begin{gathered} y-4=\frac{9}{-3}(x+2), \\ y-4=-3(x+2). \end{gathered}[/tex]Taking the above solution to its slope-intercept form, you get:
[tex]\begin{gathered} y=-3x-6+4, \\ y=-3x-2. \end{gathered}[/tex]Answer: [tex]y=-3x-2.[/tex]Spencer went to the county fair and spent his money only on ride tickets and fair admission. He bought 17 tickets for the rides and spent a total of $30.75 at a county fair. The county fair charges $1.25 per ticket for the rides and the price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets. (a) Write a linear equation that can be used to determine the cost for anyone who only pays for ride tickets and fair admission. (b) Explain your answer to Part 1a.
Answers
The linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Spencer bought 17 tickets for the rides and spent a total of $30.75 at a county fair.
Let x be the number of tickets and y be the total cost:
Total ticket cost = 17×1.25 = $21.25
Admission fari = 30.75 - 21.25 = $9.5
The linear equation is:
y = 1.25x + 9.5
Here 9.5 represents the fixed admission fair.
Thus, the linear equation y = 1.25x + 9.5 can be used to determine the cost for anyone who only pays for ride tickets and fair admission.
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3x=8y-34y+2x=5Based on the system of equations above, what is the value of x/y?
Answers
To solve the given system of equations, we can solve the first equation for x, then we combine the equations
[tex]\begin{gathered} 3x=8y-3 \\ x=\frac{8y-3}{3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 4y+2x=5 \\ 4y+2(\frac{8y-3}{3})=5 \\ 4y+\frac{16y-6}{3}=5 \\ 4y+\frac{16}{3}y-2=5 \\ \frac{12y+16y}{3}=5+2 \\ \frac{28y}{3}=7 \\ 28y=7\cdot3 \\ y=\frac{21}{28} \\ y=\frac{3}{4} \end{gathered}[/tex]So, y = 21/28.
Now, we use the y-value to find x.
[tex]\begin{gathered} x=\frac{8\cdot\frac{21}{28}-3}{3}=\frac{\frac{168}{28}-3}{3}=\frac{\frac{84}{14}-3}{3}=\frac{\frac{42}{7}-3}{3} \\ x=\frac{\frac{42-21}{7}}{3}=\frac{\frac{21}{7}}{3}=\frac{3}{3}=1 \end{gathered}[/tex]Hence, the value of each variable is x = 1 and y = 3/4.Study Surface Area and Volume of Pyramid and Cone. How to find lateral area and total surface area of pyramid? please include one(1) problem per question with solutions.
Answers
Let's apply the formula for the lateral area and total surface area of a pyramid.
• Lateral Surface Area:
To find the lateral area of a pyramid, apply the formula:
[tex]A_l=\frac{1}{2}ps[/tex]Where:
p is the perimeter of the base
s is the slant height.
Example:
From the above square base pyramid, we have:
length of base, b = 4 cm
Slant height, s = 3 cm
Let's find the lateral area.
Since the base is a square, the perimeter will be:
p = 4 x 4 = 16 cm
Hence, to find the lateral area, we have:
[tex]\begin{gathered} A_l=\frac{1}{2}ps \\ \\ A_l=\frac{1}{2}\times16\times3 \\ \\ A_l=24\operatorname{cm}^2 \end{gathered}[/tex]Therefore, the lateral area of the square base pyramid above is 24 cm².
• Total surface area of a pyramid.
To find the total surface area of a pyramid, apply the formula:
[tex]A_s=\frac{1}{2}Ps+A[/tex]Where:
A is the area of the base
p is the perimeter of the base
s is the slant height.
Or we can simply say, the formula for total surface area is:
Total surface area = Lateral area + Area of base
Example:
Using the squarea base pyramid above, we have:
Area of base = 4 x 4 = 16 cm²
Lateral area = 24 cm²
Total surface area = 24 cm² + 16 cm² = 40 cm².
Which of the following represents a compound?
H
H-3
H2O
O-16
Answers
Answer:
Step-by-step explanation:
Calculate each value requested for the following set of scores.a. ΣΧ=b. ΣΧ2=c. (ΣΧ)2=d. SS=Scores: 2, 3, 0,5Round to the hundredths place.
Answers
a.
[tex]\Sigma x=2+3+0+5=5+5=10[/tex]b.
[tex]\Sigma x^2=2^2+3^2+0^2+5^2=4+9+25=38[/tex]c.
[tex](\Sigma x)^2=(2+3+0+5)^2=10^2=100[/tex]d.
[tex]\begin{gathered} SS=\Sigma(x-\bar{x})^2 \\ where: \\ \bar{x}=\frac{2+3+0+5}{4}=\frac{10}{4}=2.5 \\ so: \\ SS=(2-2.5)^2+(3-2.5)^2+(0-2.5)^2+(5-2.5)^2 \\ SS=(-0.5)^2+(0.5)^2+(-2.5)^2+(2.5)^2 \\ SS=13 \end{gathered}[/tex]write a function to describe the following scenario.a basketball player practices jump shots. she starts at zero points and scores 5 points per minute. how many points will she have scored after a certain number of minutes?Y = ?x
Answers
number of minutes : x
number of points scored after x minutes : y
points scored per minute : 5
y=5x
multiply the points scored per minute (5) by the number of minutes (x). The expression is equal to the total number of points scored (y).
need help with this problem drop down 1, 2 dashed, soliddrop down 3 4 below, above
Answers
The boundary line is graphed as a dashed line if the symbols < or > are used, and as a solid line if the symbols ≥ or ≤ are used.
For an inequality in slope-intercept form, the half-plane above the line is shaded if the symbols > or ≥ are used, and the half-plane or ≤ are used. the line is shaded if the symbols < or ≤ are used.
Complete each proof using the properties of equality. ALL POWS W
Type the properties how they are listed above.
18; Prove: = 10
Answers
Ensuring that each person has an equal chance to maximize their potential is what equality is all about.
How is the equality property demonstrated?Proof: Given that A = B and B = C, we can infer that A = C according to the transitive principle. A = C and C = D are both true if we also know that C = D. We shall ultimately get at A = D after one more transitive property application.
The symmetrical attribute of equality
This fact, which states that if
18 + 10 =28,
then
28 = 10 + 18,
Serves as an example of the equality's symmetric property. The symmetric property of equality in mathematics is actually fairly straightforward. According to this principle, if a = b, then b =a.
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The Morgans bought a $333,000 condominium. They made a down payment of $47,000 and took out a mortgage for the rest. Over the course of 30 years theymade monthly payments of $1714.72 on their mortgage until it was paid off.(a)(b)What was the total amount they ended up paying for the condominium(including the down payment and monthly payments)?$1]How much interest did they pay on the mortgage?I need help with this math problem.
Answers
Given: The following on the purchase of a Condominium
[tex]\begin{gathered} Price(Condominium)=333000 \\ Down-payment=47000 \\ Monthly-payment=1714.72 \\ Time=30years \end{gathered}[/tex]To Determine: The total amount they ended up paying for the condominium
Solution
Please note that we have 12 months in a year. The total number of months in 30 years would be
[tex]\begin{gathered} 1year=12months \\ 30years=30\times12months \\ 3oyears=360months \end{gathered}[/tex]Total monthly payments would be
[tex]\begin{gathered} 1month=1714.72 \\ 360months=360\times1714.72=617299.20 \end{gathered}[/tex]Therefore, the total amount they ended up paying for the condominium would be the addition of the down payment and the monthly payments
[tex]Total-amount(Paid)=47000+617299.20=664299.20[/tex]Hence, the total amount they ended paying for the condominium is $664,299.20
The interest paid on the mortgage would be the difference between the total amount paid and the cost
[tex]\begin{gathered} Interest=(Total-amount-paid)-Cost(condominium) \\ =664299.2-333000 \\ =331299.20 \end{gathered}[/tex]Hence, the interest paid on the Mortgage is $331,299.20
Can someone give examples of negative exponents in the world
Eg : seize of bacteria 1*10^-4
Answers
The example of negative exponent in the real world is the world's smallest bat, the bumblebee bat weighs of 7 × 10^-2 ounces
How to illustrate the information?An exponent's sign indicates how many times to multiply or divide a base number. A negative exponent indicates the opposite.
The multiplicative inverse of the base raised to a power with the opposite sign of the provided power is referred to as a negative exponent. In plain English, we write the number's reciprocal and solve it just like positive exponents. The bat has a negative exponent.
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Find the minimum and maximum values of the function on the interval [11,27].
Answers
-4x + 0.4y = -0.8 6x + 0.4y = 4.2 The solution to the system is ( , ).
Answers
An equation is a mathematical statement created by joining two numerical or variable expressions with an equal sign, as in 3x+5=11. A number that may be entered for the variable to produce a true number statement is the answer to an equation.
Explain about the solution?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Take into account the formula 7x - 35 = 0. If we solve, we get either x = 5 or 7x = 35. The following linear equation only has one solution, x = 5, because the above linear equation is only true if x = 5.
The solution to this system (x=0.5 y=3)
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Simplify.
[3 (4-2)] x (16-4x3)
O 10
O 24
O 360
O 468
Answers
hope that help s you soooooooooooooooooo much
Using compatible numbers to estimate, which expression has a quotient of about 70?
O A. 3,424 ÷ 49
OB. 5,358 ÷ 89
O C. 6,409 ÷ 79
O D. 5,238 ÷ 89
Answers
which statements are true about points A,B, and C check all that applyA. the coordinates of point a are (3, -3)B. the coordinates of point B (1, -3)C. the coordinates of Point C are (-2,2)D. Point C is the closest to the Y axisE. points A and B are the same distance from the y-axisIk the pic is blurry sorry
Answers
By the graph, we can see that the only statement that apply is B. the coordinates of point B is (1, -3).
A student must have an average (the mean) on five tests that is greater than or equal to 80% but less than 90% to receive a final grade of B. Devon’s grades on the first four tests were 76%, 65%, 89%, and 80%. What range of grades on the fifth test would him a B in the course? ( Assume that 100% is the highest grade possible.)
Enter the range of grades necessary for Devon to earn a b average.
__% < x < 100%
- -
Answers
Answer:
90% ≤ x ≤ 100%Step-by-step explanation:
Test results are:
76, 65, 89, 80 and x.The average of 5 tests should be:
80 ≤ average < 90, to get a B.The average is:
(76 + 65 + 89 + 80 + x)/5 = (310 + x)/5Plug it into inequality:
80 ≤ (310 + x)/5 < 90 Multiply by 5400 ≤ 310 + x < 450 Subtract 31090 ≤ x < 140But the maximum possible result from one test is 100%, considering this top score Devon must get:
90% ≤ x ≤ 100%If the links in a 30-inch necklace each measure three-eights of an inch long, how many links would be in then necklace?
Answers
ANSWER
80 links
EXPLANATION
To find how many links would be in the necklace, we have to divide the total length of the necklace, 30 inches, by the length of each link, 3/8 inch,
[tex]30\div\frac{3}{8}[/tex]Use the KCF method:
• K,eep the first fraction
,• C,hange the division sign into a multiplication sign
,• F,lip the second fraction,
[tex]30\div\frac{3}{8}=30\times\frac{8}{3}[/tex]30 and 3 can be simplified - 30 is 3 times 10,
[tex]30\times\frac{8}{3}=10\times8=80[/tex]Hence, the necklace would have 80 links.
