The cost of a pack of gum bought by Lionel is $2.1.
Let the variable g represent the cost of a pack of gum.
Let the variable c represent the cost of a candy bar.
Since Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80, a linear equation that models this situation is;
4c + 2g = 9.80 ......equation (1)
Additionally, two packs of gum cost the same as three candy bars:
2g = 3c ......equation (2)
c = 2g/3 ......equation (3)
Substituting equation (3) in equation (1), we get:
4(2g/3) + 2g = 9.80
8g/3 + 2g = 9.80
14g/3 = 9.80
14g = 29.4
= 29.4/14
= $2.1
The cost of a pack of gum is $2.1.
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The complete question is -
Lionel bought 4 candy bars and 2 packs of gum at the gas station and spent $9.80. Two packs of gum cost the same as three candy bars. Let g represent the cost of a pack of gum and c represent the cost of a candy bar. What is the cost of a pack of gum?
Bob made 15,000 in taxable income lat year. Suppoe the income tax rate i 15% for the firt 8000 plu 19% for the amount over 8000. How much mut Bob pay in income tax for lat year?
Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.
What is taxable income?The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.
Define revenue.Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.
The first $8000 of Bob's taxable income is taxed at 15%:
Tax on first $8000 = $8000 * 0.15 = $1200
The remaining $7000 of Bob's taxable income is taxed at 19%:
Tax on remaining income = $7000 * 0.19 = $1330
Total tax = $1200 + $1330 = $2530
So Bob must pay $2530 in income tax for last year.
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Help please! Thank you
Answer:
the answer is z^2-9. Using the box method line up equation. Then multiple numbers outside of the box and put numbers inside. Lastly combine like terms.
Colorado State Flag (7. 4. A. 1. 4)
Illustrative Mathematics
1. 4: Colorado State Flag
The side lengths of the state flag of Colorado are in the ratio 2:3. If a flag is 12 feet long, what is its height?
The height of the flag is 18 feets.
What is a rectangle?Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Length is equal to 2 (2 + 3) the sum of the side lengths.
The sum of side length divided by (12) equals (2/5)
12 = 0.4(sum of side length) (sum of side length)
divide both sides by 0.4.
The height of the flag is calculated as side lengths plus length.
Height of flag: (30 – 12) = 18 feet
Therefore, the height of the flag is 18 feets.
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quadratic expression x² +6x +5
Answer:
if its for factor, we have (x+1)(x+5), if its for formula, its x=-1, -5
Step-by-step explanation:
The first figure is dilated to form the second figure!
Which statement is true?
The scale factor is 0.25
The scale factor is
The scale factor is 4.35
The scale factor is 7.25
The first figure is dilated to form the second figure, the statement according to will be the scale factor is 0.25.
What is ratio?The ratio notion is used in mathematics when evaluating two or more numbers. It works as a comparison tool to demonstrate how big or small a particular number is.
A ratio divides two quantities in order to compare them.
As per the given information in the question,
We have two side lengths,
First figure: This represents the object length, which is a diamond with a length equal to 5.8.
Second figure:The picture length is then represented by a small diamond with sides that measure 1.45.
So, the scale factor is,
k = Image length/Object length
k = 1.45/5.8
k = 0.25.
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What does exponential growth look like on a logarithmic graph?
Exponential growth on a logarithmic graph looks like a straight line. On a regular graph, the line would appear to be curved, but when plotted on a logarithmic graph, the line appears to be a straight line.
Exponential growth on a logarithmic graph appears as a straight line. This is because the logarithmic scale is a compressed scale, meaning that it takes a large range of values and compresses them into a smaller range. This makes the data easier to read and understand. The straight line occurs because the logarithmic scale is designed to fit the data points more closely, making the line appear linear. This is in contrast to the regular scale, where the line appears curved due to the large range of values being plotted. Thus, exponential growth appears as a straight line on a logarithmic graph.
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In the diagram below, \overline{MN}
MN
is parallel to \overline{JK}
JK
. If MNMN is 1212 more than LNLN, LK=33LK=33, and JK=55JK=55, find the length of \overline{LN}
LN
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing length LN of the similar triangles is; LN = 18
How to solve Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.
In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;
LN/LK = MN/JK
We are told that;
MN is 12 more than LN. Thus; MN = 12 + LN
LK = 33
JK = 55
Thus;
LN/33 = (12 + LN)/55
55LN = 33(12 + LN)
55LN = 396 + 33LN
22LN = 396
LN = 396/22
LN = 18
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The N71-90 virus will give an infected person a mild rash on their arms once the person has 1 billion of the virus cells in their body. After an initial infection with just one cell, each virus cell will divide into two cells every four hours. After 30 divisions there are 1,073,741,824 cells and the rash starts. Once the rash starts, the immune system kicks in and kills all of the virus cells within an hour. The number of virus cells in the body can be determined using the function where h is the number of hours after infection. If Jolene is infected by one virus cell, how many virus cells will she have after 12 divisions
Jolene will have 4096 virus cells in her body after 12 divisions
Why should we call viruses a cell?Viruses are something more than living or dead, they are both. Maybe we need a new classification of life for them, a life that lives when the environment is favorable and hibernate when it is not.
The function provided to determine the number of virus cells in the body after h hours is 2^h. To find the number of virus cells after 12 divisions, we can plug in 12 for h in the function.
2^12 = 4096.
So, Jolene will have 4096 virus cells in her body after 12 divisions.
Please note that Jolene would not develop a rash after 12 divisions as it would take 30 divisions (120 hours) for the rash to appear.
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Can you help me with this
The linear function that passes through (3,1) and has a slope of -1/2 is defined as follows:
y = -0.5x + 2.5.
The graph of the linear function is given by the image presented at the end of the answer.
How to define the linear function?The linear function for this problem is defined in slope-intercept format, as follows:
y = mx + b.
In which the coefficients of the function are given as follows:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the y-intercept, representing the value assumed by the output variable y when the input variable x assumes a value of zero.The slope of the function in this problem is given as follows:
m = -1/2 = -0.5
Hence:
y = -0.5x + b.
The line passing through point (3,1) means that when x = 3, y = 1, and thus the intercept b is obtained as follows:
1 = -0.5(3) + b
1 = -1.5 + b
b = 2.5.
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Is 4 a polynomial or not?
The term given to us is 4 , this is a constant number therefore this cannot be regarded as a polynomial.
An expression is said to be a polynomial if it also contains a variable along with constants which are joined with each other through various mathematical operations. These expressions usually have more than one terms.
A polynomial can be of various degrees such as one degree , two degree based upon that they are known as linear , quadratic , cubic polynomial etc. Unlike terms are polynomial terms in which the variables are different and also the same variables with different powers. Contrary terms are two or more terms that are not synonymous.
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Using traditional methods it takes 8.5 hours to receive a basic flying license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 21 students and observed that they had a mean of 8.8 hours with a variance of 1.21. Is there evidence at the 0.05 level that the technique performs differently than the traditional method? Assume the population distribution is approximately normal. Step 1 of 5 : State the null and alternative hypotheses
There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
What are the hypothesis tested?At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:
[tex]H_0: \mu = 8.5[/tex]
At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:
[tex]H_1: \mu \neq 8.5[/tex]
We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:
|z| = 1.96.
(p-value of 1 - (0.05/2)).
Hence the decision rule is given as follows:
|z| < 1.96 -> do not reject the null hypothesis -> not enough evidence.|z| > 1.96 -> reject the null hypothesis -> enough evidence.What is the test statistic?The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.
The equation is given as follows:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.The parameters for this problem are given as follows:
[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]
Hence the test statistic is of:
[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]
z = 1.24.
|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.
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If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
The measure of angle B is 107°.
What do similar triangles mean?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given a triangle, NPZ is similar to triangle HBZ.
Which can also be written as ΔNPZ ≈ ΔHBZ
So, by equating the corresponding angles that are angle P = angle B:
8x-37°=180-(2x-5+42)°
10x=180
x=18°
So, H=36-5=31°
Since the sum of all angles in a triangle is 180°, angle B can be calculated as
B= 180°-(42+31)°
B=107°
Therefore the measure of angle B is 107 degrees
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Question Progress
Here are some temperatures.
Ottawa
New York
Oslo
Moscow
-9.5 °C
-11.6 °C
-4.3 °C
-7.9 °C
a) Which place has the highest temperature?
b) What is the difference in temperature between Ottawa and Oslo?
The temperature in Moscow falls by 3.1°C.
c) What is the new temperature in Moscow?
The place with the highest temperature is Oslo.
The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .
The new temperature in Moscow is 11 degrees Celsius .
How to find the temperature ?When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.
The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:
= - 4 . 3 - ( - 9 . 5 )
= - 4.3 + 9 .5
= 5. 2 degrees Celsius
The new temperature in Moscow is:
= - 7.9 - 3.1
= 11 degrees Celsius
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How does the value of a number change when you divide by 10 100 1000?
Answer: It gets smaller
Step-by-step explanation: When you divide something by anything, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.
b) Sita had.50 sweets. She ate 10 sweets and gave 8 sweets to her brother. If she divided the rest of them among her 8 friends equally, how many sweets would each friend get?
Answer:
4 sweets each
Step-by-step explanation:
50 sweets to begin with and eats 10 , so 50 - 10 = 40 left
she then gives 8 to her brother , leaving 40 - 8 = 32 sweets
she then shares 32 equally among her 8 friends , so
32 ÷ 8 = 4
that is each friend got 4 sweets
whats the awnser i need help
answer:10
Step-by-step explanation:
the graph show it is 1 hour and shows 10 miles and it continues
Answer:
it should be that the miles are 10 times the amount of hours
Step-by-step explanation:
Considering that to bike 10 miles it took 1 hour and to bike 20 miles it took 2 hours it will continue going like that so the miles will always be 10 times the amount of hours
Where does the line 2x 3y 6 will intersect Y axis at?
The graph of the given line 2x+3y=6 intersects the Y-axis at (0,2).
For the graph of linear equation to intersect the Y-axis, its X-co-ordinate should be zero or the abscissa is zero as Y-axis as the equation of Y-axis is x=0. Also the set of coordinates should satisfy the equation.
According to the first condition the x-coordinate of the equation should be zero so in equation 2x+3y=6 substituting the value of x as zero 2(0)+3y=6
3y=6
y=6/3=2
So at point (0,2), the graph of the given line 2x+3y=6 intersects the Y-axis.
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I need help with this, please
A Triangle has two sides of length 16.4 and 10.2. What compound inequality describes the possible length for the 3rd side
Answer:
6.2 < x < 26.6
Step-by-step explanation:
The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.
16.4 - 10.2 = 6.2
16.4 + 10.2 = 26.6
Let x = length of third side.
6.2 < x < 26.6
What does += mean in Python?
In Python an operator += is an assignment operator which adds the value on its right to the variable and assigns the result to the variable on its left.
We know that an operator is a symbol that represents a mathematical or logical process.
We know that in Python the operator += provides a convenient way to add a value to an existing variable and assign the new value back to the same variable.
If p += q
This means, the variable p the left side is getting added to the value on the right side (q), and the result is then reassigned to the variable on the left.
i.e., p = p + q
+= is an assignment operator.
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Click on the assignment icon to receive a printout of this construction assignment. Do the assignment and be ready to give it to your teacher for grading if it is requested.
The Construction is shown below.
What is Perpendicular line?Perpendicular lines are lines that intersect at a right (90 degrees) angle.
Given:
a) Steps for perpendicular line:
To cross the line segment, draw two arcs.Create two more intersecting arcs.Connect the initial point to the intersection of the arcs.b) Perpendicular Bisector for triangle
Draw arcs with the same radius that are centered at X and Y by opening the compass more than halfway.These two arcs come together at two locations. They will be referred to as points P and Q.The line segment M, which is the perpendicular bisector of the line segment S, should be drawn by placing the ruler where the arcs meet (that is, by connecting points P and Q).we are going to proceed in the same way on all three sides of the triangle to draw its three perpendicular bisectors (Ma, Mb and Mc)So, if we extend the bisector they can meet inside, at center and outside the triangle.
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77:9 =
nt :
is there anyone named christina mansell?
Christian Mansell (born 9 February 2005) is an Australian racing driver set to compete in the 2023 FIA Formula 3 Championship with Campos Racing. He previously competed in the 2022 Neuroforamina Open Championship for Crypto Tower Racing, finishing in third overall in the standings.
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What is the quotient of 1. 782 x 109 and 8. 1 x 106 expressed in scientific
notation?
The quotient of 1.782 × 10⁹ and 8.1 × 10⁶ in scientific notation is 2.2 × 10². The result is obtained by using the quotient rule.
What are the rules for exponents?Several rules for exponents are
Product rule → aⁿ × aˣ = aⁿ⁺ˣQuotient rule → aⁿ / aˣ = aⁿ⁻ˣPower of a product rule → (ab)ⁿ = aⁿ × bⁿPower of a quotient rule → (a/b)ⁿ = aⁿ / bⁿPower of a power rule → (aⁿ)ˣ = aⁿˣZero rule → a⁰ = 1Find the quotient of 1.782 × 10⁹ and 8.1 × 10⁶!
Dividing the first number by the second using the quotient rule, it would be
= (1.782 × 10⁹) / (8.1 × 10⁶)
= (1.782/8.1) × (10⁹/10⁶)
= 0.22 × 10⁹⁻⁶
= 0.22 × 10³
In scientific notation, we should write a.b × 10ⁿ, where 1 ≤ a < 10 and n is an integer.
So,
0.22 × 10³ = 2.2 × 10²
Hence, the result of 1.782 × 10⁹ divided by 8.1 × 10⁶ in scientific notation is 2.2 × 10².
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What range of values is not a possible scale factor (k)?
A) k 1
D) all are possible
A range of values which is not a possible for scale factor (k): k = 0
We know that the scale factor is the number (also called the conversion factor) which is used to change the size of a figure without changing its shape.
It is used to expand or compress the size of an object.
The scale factor formula is:
Scale factor = Dimensions of the transformed shape ÷ Dimensions of the original shape
If the scale factor k > 1, the object is enlarged.
If the scale factor is 0< k <1, the object is compressed.
If the scale factor is k = 1, the shape of object remains the same.
And the scale factor cannot be zero.
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EMERGENCY NEED HELP PLEASE HELP THE QUESTION IS ATTACHED TO THE QUESTION THING PLEASE HELP!!!
Graph of given system of equations is shown in figure with intersection point (2, 4).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The system of equation is,
⇒ 2x + y = 8
⇒ - x + 2y = 6
By solving both equation , we get;
⇒ (x, y) = (2, 4)
Thus, The graph of system of equation intersect on point (2, 4).
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Find the area of the front face of the shed. Please help asap.
Answer:
8.25cm²
Step-by-step explanation:
the area of the triangle = (half x base x height )=
(1.5x3)÷2= 2.25cm²
the area of the rectangle= length x width = 3x2= 6cm²
total = 2.25+6= 8.25cm²
how to solve inequations
Answer:
When solving an inequality: you can add the same quantity to each side •you can subtract the same quantity from each side you can multiply or divide each side by the same positive quantity If you multiply or divide each side by a negative quantity, the inequality symbol must be reversed.
you can add subtract multiply and divide the quantity to each side
But if you’re doing any of those with a negative quantity, the inequality symbol must be reversed
3 x -8> 29
3 x -8 < 29
In 2017 the Hindu festival of Diwali occurred on Thursday, 19 October. What fraction of the year was this
The Diwali occurred on 0.408 or 40.8% of the year in 2017.
To find the fraction of the year that Diwali occurred in 2017, we need to divide the number of days between Diwali and the start of the year by the total number of days in the year.
Diwali occurred on Thursday, October 19, 2017. The start of the year 2017 is January 1, 2017 which is a Sunday.
There are 365 days in a non-leap year. Since 2017 is not a leap year, there are 365 days in that year.
So the fraction of the year that Diwali occurred in 2017 can be calculated as: (days between Diwali and the start of the year) / (total days in the year) = ( 19 + 31 + 30 + 31 + 30 + 19 ) / 365 = (148) / 365 = 0.408
So, the Diwali occurred on 0.408 or 40.8% of the year in 2017.
Therefore, Diwali occurred on 0.408 or 40.8%
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How do you calculate the number of seeds per acre?
1. Convert lb./acre to grams/acre
2. Use the TKW to calculate seeds per acre.
What is acre?The imperial system and US customary systems both use acres as a measure of land area.
According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.
A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.
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15 In circle F with m/EFG = 78 and EF = 4 units, find the length of arc EG. Round to the nearest hundredth. F G E
Length of arc EG = 5.446 degrees and EG = 0.05446 degrees while written in hundredth.
What means arc length of a circle?Arc length is defined as the distance of two points along the boundary of a circle or a section of a curve. Arc length is not a straight line.
Arc length is calculated by the following formula.
arc length in radians
s = r Ф
where, r is radius of circle or curve
Ф is the central angle in radians
arc length is degrees
s = Ф×π/180 × r
r is the radius of circle
Ф is the central angle in degrees
π = 3.142
How to calculate the arc length in the given problems?given, central angle EFG = 78 degrees.
EF = 4 units
EF is the radius of the given circle
as per the rules of a circle FG is also a radius
FG = FE = 4 units
Now arc length EG = ∠EFG × π/180 × EF
Arc length = 78 × 3.142/180 × 4
=5.446 units
hence, arc length EG = 5.446 units or 5.446 degrees
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