Choosing two math instructors out of 8 would be
[tex]P=\frac{2}{8}=\frac{1}{4}[/tex]Choosing two science instructors out of 10 would be
[tex]P=\frac{2}{10}=\frac{1}{5}[/tex]Given that they are independent events, we multiply their probabilities
[tex]P=\frac{1}{4}\times\frac{1}{5}=\frac{1}{20}[/tex]Hence, the probability of selecting two math instructors and two science instructors is 1/20.
The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21
decide wether the following sides are acute obtuse or a right triangle.
The acute triangle is defined by the condition,
[tex]a^2+b^2The obtuse triangle is defined by the condition, [tex]a^2+b^2>c^2[/tex]Here, we have,
[tex]\begin{gathered} 19^2=361 \\ 12^2=144 \\ 15^2=225 \\ 12^2+15^2>19^2 \end{gathered}[/tex]Thus, the triangle is an obtuse triangle.
A rectangular sheet of metal is 40 inches wide and 100 inches long. What is its perimeter?
Explanation
We are given the following:
[tex]Rectangle\begin{cases}width={\text{ }40inches} \\ length={\text{ }100inches}\end{cases}[/tex]We are required to determine the perimeter of the rectangular sheet.
This is achieved thus:
We know that the perimeter of a rectangle is given as:
[tex]P=2(l+w)[/tex]Therefore, we have:
[tex]\begin{gathered} P=2(100+40) \\ P=2(140) \\ P=280inches \end{gathered}[/tex]Hence, the answer is:
[tex]280inches[/tex]Find the next two numbers in the pattern -243, 81, -27, 9
Find the next two numbers in the pattern -243, 81, -27, 9
Notice that all the values in the series are value of 3 raise to the power of a number.
-243 =
Nora has a job where she has a take home salary each month of $2400. if Nora wants to spend no more than 15% of her monthly take home salary on her car payment, how much can she afford?
Her take home salary is $2400 and she wants to spend no more than 15% on her car payment. Therefore, she can afford no more than 0.15*2400 = $360 on her car payment.
(Please show your work for question 18.)
It is given that AB = CB from this information we conclude that <A=<C by reason :angles opposite equal sides.
<A+<B+<C=180°(Sum of angles in a triangle)
[tex](4x - 13) + (5x - 2) + (4x - 13) = 180 \\ 4x + 5x + 4x - 13 - 2 - 13 = 180 \\ 13x - 28 = 180 \\ 13x = 180 + 28 \\ 13x = 208 \\ \frac{13x}{13} = \frac{208}{13} \\ x = 16[/tex]
x=6°
ATTACHED IS THE SOLUTION
GOODLUCK
the double number line shows the price of one cupcake complete the table and show the same information as a double number line 5 to blank blank to 18 and 18 to blank
From the first diagram shown, we can see that 1 cupcake costs $1.5
To get the price of 5 cupcakes
Since 1cupcake = $1.5
5 cupcakes = $x
cross multiply
1 * x = 5 * 1.5
x = $7.5
Hence 5 cupcakes will cost $7.5
Since 1cupcake = $1.5
18 cupcakes = $x
cross multiply
1 * x = 18 * 1.5
x = $27
Hence 5 cupcakes will cost $27
To get the number of cupcakes priced $18
Since 1cupcake = $1.5
x cupcake = $18
1.5x = 18
divide both sides by 1.5
1.5x/1.5 = 18/1.5
x =
The perimeter of the rectangle is 19.4 centimeters.What is the width in centimeters,of the rectangle Length is 6cm
SOLUTION
From the question, the Perimeter of the rectangle is 19.4 cm and we want to find the width. The perimeter of a rectangle is given by
[tex]\begin{gathered} P=2\left(l+w\right) \\ where\text{ P =perimeter = 19.4} \\ l=length\text{ of rectangle = 6 cm} \\ w=width=? \end{gathered}[/tex]Applying this, we have
[tex]\begin{gathered} P=2\left(l+w\right) \\ 19.4=2\left(6+w\right) \\ 19.4=12+2w \\ 2w=19.4-12 \\ 2w=7.4 \\ w=\frac{7.4}{2} \\ w=3.7 \end{gathered}[/tex]Hence the width is 3.7 cm, option C
$85000 is invested at 7.5% per annum simple interest for 5 years. Calculate the simple interest.
From the statement of the problem we know that:
• the principal amount of money invested is P = $85000,
,• the rate per year is 7.5%, in decimals r = 0.075,
,• the time is t = 5 years.
The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:
[tex]I=A-P=P(1+r\cdot t)-P=P\cdot r\cdot t.[/tex]Replacing by the data of the problem we find that the simple interest is:
[tex]I=85000\cdot0.075\cdot5=31875.[/tex]Answer
The simple interest is $31875.
H D 2 cm 4 cm The two rectangles below are similar. What is the ratio of the perimeters of rectangle ABCD to rectangle EFGH? B А 4 cm E 8 cm F 2:1 8:1 1:4 1:2 2
In order to determine the ratio of the perimeters for the given rectangles, first calcualte their perimeters. Use the following formula:
P = 2w + 2l
w: width
l: length
For the smaller rectangle you have:
w = 2cm
l = 4 cm
P = 2(2cm) + 2(4cm) = 4cm + 8cm = 12cm
For the bigger triangle you have:
w' = 4cm
l' = 8cm
P' = 2(4cm) + 2(8cm) = 8cm + 16cm = 24cm
Then, you have:
P/P' = 12cm/24cm = 1/2
Hence, the ratio is 1:2
Suppose the purr of a cat has a sound intensity that is 320 times greater than the threshold level. Find the decibel value for this cats purr. Round to the nearest decibel.
The decibel value for this cats purr round to the nearest decibel is; 25
How to calculate the decibel level?Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.
Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.
The loudness of a sound, in decibels, with intensity I is given by;
dB = 10 log₁₀(I/I₀)
We are given the intensity of a cat’s purr as I = 320I₀
Thus;
dB = 10 log₁₀(320I₀/I₀)
dB = 10 log₁₀(320)
dB = 25.05 ≈ 25
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Find the volume of 12 cm
Answer:
1728 cm ^ 3.
Step-by-step explanation:
we are given 12 cm
As we know formula of volume of cube = s ^3 ( side * side * side ) So = 12 * 12* 12 = 1728 cm ^ 3.
Find the Volume cylinder (8cm) (12cm) h = 8cm r = 12cm h = 8 cm r = 12 cm. The volume of a cylinder is equal to the area of the base πr2 π r 2 times the height. π⋅(radius)2 ⋅(height) π ⋅ ( r a d i u s) 2 ⋅ ( h e i g h t) Substitute the values of the radius r = 12 r = 12 and height h = 8 h = 8 into the formula to find the volume of the cylinder
P.s hopes this helps
# 8 Write an equation in slope-intercept form to represent the line parallel to y = -3/4 x + 1/4 passing through the point (4, -2). O y = -3/4x + 1 O y y = 4/3x + 20/3 O y = -3/4 - 2 O y=-3x - 2
If the line is parallel to y = -3/4 x + 1/4 then the slope is -3/4
the form of an equation is y = mx +b
In this case m = -3/4
Using the point given (4, -2) we will find the value of b:
y = mx + b
y = -3/4 x + b
Using the values of the point (4, -2).... x = 4 and y = -2
-2 = (-3/4)(4) + b
Solving for b:
-2 = -3 + b
-2 + 3 = b
1 = b
b = 1
Therefore the equation would be:
y = (-3/4)x + 1
Answer:
y = (-3/4)x + 1
Solve x^2 - 3x - 10 = 0 by factoring. *Mark only one oval.O {-5,2}O (-2,-5)O {-2,5}○ {-10,1}
In order to solve this quadratic equation by factoring, we can do the following steps:
[tex]\begin{gathered} x^2-3x-10=0\\ \\ x^2-3x-5\cdot2=0\\ \\ x^2+2x-5x-5\cdot2=0\\ \\ x(x+2)-5(x+2)=0\\ \\ (x-5)(x+2)=0\\ \\ \begin{cases}x-5=0\rightarrow x=5 \\ x+2=0{\rightarrow x=-2}\end{cases} \end{gathered}[/tex]Therefore the solution is {-2, 5}. Correct option: third one.
I have to create a graph but I need some help and clarification
To complete the table you evaluate the equation by the given value of x to find the corresponding value of y:
[tex]y=x+4[/tex][tex]\begin{gathered} x=4 \\ \\ y=4+4 \\ y=8 \\ \\ (4,8) \end{gathered}[/tex][tex]\begin{gathered} x=8 \\ \\ y=8+4 \\ y=12 \\ \\ (8,12) \end{gathered}[/tex][tex]\begin{gathered} x=12 \\ \\ y=12+4 \\ y=16 \\ \\ (12,16) \end{gathered}[/tex][tex]\begin{gathered} x=16 \\ \\ y=16+4 \\ y=20 \\ \\ (16,20) \end{gathered}[/tex]To put those (x,y) points in the plane;
the frist coordinate x is the number of units you move to the left (if x is negative) or to the right (if x is positive)
the second coordinate y is the number of units you move down (if y is negative) or up (if y is positive)
Then, using the points (0,4), (4,8), (8,12), (12,16) and (16,20) you get the next graph for y=x+4:
1 1 10 1 b. What fraction of the whole square is shaded? Explain how you know.
1/100
Explanation:To get the fraction of the square shaded we would use the rows and columns
For the row:
The total on the 1st row = 1
The first row is divided into 10. This means each box in the first row: 1/10
One of the box is shaded. This implies the fraction shaded in the first row is 1/10
For the column:
The total on the 1st column = 1
The column is also divided into 10 box which means each box represent 1/10
Since one of the box in the column is shaded, it represent 1/10
Fraction of the whole square shaded = fraction shaded in the row × fraction shaded in the column
Fraction of the whole square shaded = 1/10 × 1/10
Fraction of the whole square shaded = 1/100
the variable y is directly proportional to x. if y equals -0.6 when x equals 0.24, find x when y equals -31.5.
You have that y is proportional to x. Futhermore, you have y = -0.6 when x = 0.24.
Due to y is proportional to x, you have the following equation:
[tex]y=kx[/tex]where k is the constant of proportionality. In order to find the value of x when y = -31.5, you first calculate k.
k is calculated by using the information about y=-0.6 and x=0.24. You proceed as follow:
y = kx solve for k
k = y/x replace by known x and y values
k = -0.6/0.24
k = -2.5
Hence, the constant of proportionality is -2.5.
Next, you use the same formula for the relation between y and x to find the value of x when y = -31.5. You proceed as follow:
y = kx solve for x
x = y/
find the exact values of the six trigonometric functions of the angle 0 shown in the figure(Use the Pythagorean theorem to find the third side of the triangle)
The right angled triangle is given with reference angle theta.
The opposite side (facing the reference angle) is 3, while the hypotenuse (facing the right angle) is 5. The adjacent shall be calculated using the Pythagoras' theorem as follows;
[tex]\begin{gathered} \text{Adj}^2+3^2=5^2 \\ \text{Adj}^2=5^2-3^2 \\ \text{Adj}^2=25-9 \\ \text{Adj}^2=16 \\ \text{Adj}=\sqrt[]{16} \\ \text{Adj}=4 \end{gathered}[/tex]Therefore, the trigonometric functions of angle theta are shown as follows;
[tex]\begin{gathered} \sin \theta=\frac{opp}{hyp}=\frac{3}{5} \\ \cos \theta=\frac{adj}{hyp}=\frac{4}{5} \\ \tan \theta=\frac{opp}{adj}=\frac{3}{4} \\ \csc \theta=\frac{hyp}{opp}=\frac{5}{3} \\ \sec \theta=\frac{hyp}{adj}=\frac{5}{4} \\ \cot \theta=\frac{adj}{opp}=\frac{4}{3} \end{gathered}[/tex]Consider the parabola given by the equation: f ( x ) = − 2 x 2 − 12 x − 9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list of points of form (x, y) separated by commas: It is OK to round your value(s) to to two decimal places.
Answer:
it is C) find the coordinated of two x intercept is
A local children's center has 46 children enrolled, and 6 are selected to take a picture for the center'sadvertisement. How many ways are there to select the 6 children for the picture?
The question requires us to find how many ways we can select 6 children from a total of 46.
The formula for combinations is given as follows;
[tex]nC_r=\frac{n!}{(n-r)!r!}[/tex]Where n = total number of children, and r = number of children to be selected. The combination now becomes;
[tex]\begin{gathered} 46C_6=\frac{46!}{(46-6)!6!} \\ 46C_6=\frac{46!}{40!\times6!} \\ 46C_6=\frac{5.5026221598\times10^{57}}{8.1591528325\times10^{47}\times720} \\ 46C_6=\frac{5.5026221598\times10^{10}}{8.1591528325\times720} \\ 46C_6=\frac{0.674410967996781\times10^{10}}{720} \\ 46C_6=\frac{6744109679.967807}{720} \\ 46C_6=9,366,818.999955287 \\ 46C_6=9,366,819\text{ (rounded to the nearest whole number)} \end{gathered}[/tex]In the diagram below, GD = 10.1,EF 28.1, and EG 16.9. Find the length==of FC. Round your answer to the nearest tenthif necessary.
Solution:
In the figure;
[tex]\begin{gathered} \frac{EG}{EF}=\frac{ED}{EC} \\ \\ EG=16.9,ED=27,EF=28.1 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} \frac{16.9}{28.1}=\frac{27}{EC} \\ \\ EC=44.9 \end{gathered}[/tex]Thus;
[tex]\begin{gathered} FC=EC-EF \\ \\ FC=44.9-28.1 \\ \\ FC=16.8 \end{gathered}[/tex]A family is traveling from their home to avacation resort hotel. The table below showstheir distance from home as a function of time.Time (hrs)0257Distance(mi)0140375480Determine the average rate of change betweenhour 2 and 7, including the units.
Let
x -------> the time in hours
y -------> the distance in miles
we know that
To find the average rate of change, we divide the change in the output (y) value by the change in the input value (x)
so
For x=2 h ------> y=140 mi
For x=7 h ------> y=480 mi
rate of change=(480-140)/(7-2)
rate of change=340/5=68 mi/h
The average rate of change is equal to the speed in this problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Problem
144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?
Solution
for this case we can do the following proportional rule:
4/144 = x/100
And solving for x we got:
x= 100 (4/144)= 2.77
So between 2 and 3 grape fruits are expected
URGENT!! ILL GIVE
BRAINLIEST!!!!! AND 100 POINTS!!!!!
Answer:
√52
Step-by-step explanation:
[tex] \sqrt{ {(4 - ( - 2))}^{2} + {(1 - ( - 3))}^{2} } [/tex]
[tex] \sqrt{ {6}^{2} + {4}^{2} } = \sqrt{36 + 16} = \sqrt{52} [/tex]
3.2 x 104 bacteria are measured to be in a dirt sample that weighs 1 gram. Usescientific notation to express the number of bacteria that would be in a sampleweighing 21 grams.
The number of bacteria that weighs 1 gram are,
[tex]3.2\times10^4[/tex]Determine the number of bacteria in a sample that weighs 21 grams.
[tex]\begin{gathered} 21\cdot3.2\times10^4=67.2\times10^4 \\ =6.72\times10^5 \end{gathered}[/tex]So answer is,
[tex]6.72\times10^5[/tex]HELP PLEASE!!!!!!!!!!! ILL MARK BRAINLIEST
the rational number :
-1 ³/₄ is located as point 1
14/8 is located as point 5
1.125 is located as point 6
-0.875 is located as point 4
What is number line ?
Number line is virtual representation of numbers along with coordinates axis with number equally spaced with equal number of interval.
Here,
the rational number -1 ³/₄ is located as point 1, as -1 ³/₄ is greater then -1 and less then -2 on number line and is 3/4 of the gap between -1 and -2.
the rational number 14/8 is located as point 5, as 14/8 is greater then 0 and less then 1 on number line and is 3/4 of the gap between 0 and 1.
the rational number 1.125 is located as point 6, as 1.125 is greater then 1 and less then 2 on number line and is 1/8th of the gap between 1 and 2.
the rational number -0.875 is located as point 4, as -0.875 is greater then 0 and less then -1 on number line and is 1/8 th of the gap between -1 and 0.
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Canvas that costs 3/4 cents/in squared is used to make golf bags. Find the cost (in dollars) of 200 rectangular pieces of canvas, each 6.0 in. by 4.0 in.
The cost of 200 rectangular pieces of canvas given its dimensions is $36.
What is the cost?The first step is to determine the area of one of the rectangular pieces. A rectangle is a two-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
6 X 4 = 24 in²
The next step is to determine the area of the 200 rectangular pieces.
Area of the 200 rectangular pieces = 200 x 24in² = 4,800 in²
The last step is to determine the cost of the 200 rectangular pieces.
Total cost = total area x cost per squared inches
3 / 4 x 4800 = 3600 cents = $36
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Irlene has just returned from a business trip in Britain with £200 of uncashed traveller's cheques. How much would she receive from the bank when she converts the currency back to Canadian dollars, assuming that the bank offers an exchange rate of C$1.00 = £0.5544 and charges a 0.65% fee to convert the traveller's cheques to Canadian funds? For full marks your answer(s) should be rounded to the nearest cent.
The converted money in Canadian dollars is $111.6.
Given that, Irlene has just returned from a business trip in Britain with £200 of uncashed traveler's cheques.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the converted Canadian dollars be x.
x = 200 × 0.5544 + 0.65% of 200 × 0.5544
= 110.88 + 0.0065 × 110.88
= 111.60072
≈ 111.6
Therefore, the converted money in Canadian dollars is $111.6.
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^3 sq root of 1+x+sq root of 1+2x =2
The given equation is
[tex]\sqrt[3]{1+x+\sqrt{1+2x}}=2[/tex]First, we need to elevate each side to the third power.
[tex]\begin{gathered} (\sqrt[3]{1+x+\sqrt{1+2x}})^3=(2)^3 \\ 1+x+\sqrt{1+2x}=8 \end{gathered}[/tex]Second, subtract x and 1 on both sides.
[tex]\begin{gathered} 1+x+\sqrt{1+2x}-x-1=8-x-1 \\ \sqrt{1+2x}=7-x \end{gathered}[/tex]Third, we elevate the equation to the square power to eliminate the root
[tex]\begin{gathered} (\sqrt{1+2x})^2=(7-x)^2 \\ 1+2x=(7-x)^2 \end{gathered}[/tex]Now, we use the formula to solve the squared binomial.
[tex](a-b)=a^2-2ab+b^2[/tex][tex]\begin{gathered} 1+2x=7^2-2(7)(x)+x^2 \\ 1+2x=49-14x+x^2 \end{gathered}[/tex]Now, we solve this quadratic equation
[tex]\begin{gathered} 0=49-14x+x^2-2x-1 \\ x^2-16x-48=0 \end{gathered}[/tex]We need to find two number which product is 48 and which difference is 16. Those numbers are 12 and 4, we write them down as factors.
[tex]x^2-16x-48=(x-12)(x+4)[/tex]So, the possible solutions are
[tex]\begin{gathered} x-12=0\rightarrow x=12 \\ x+4=0\rightarrow x=-4 \end{gathered}[/tex]However, we need to verify each solution to ensure that each of them satisfies the given equation. We just need to evaluate it with those two solutions.
[tex]\begin{gathered} \sqrt[3]{1+x+\sqrt{1+2x}}=2\rightarrow\sqrt[3]{1+12+\sqrt{1+2(12)}}=2 \\ \sqrt[3]{13+\sqrt{1+24}}=2 \\ \sqrt[3]{13+\sqrt{25}}=2 \\ \sqrt[3]{13+5}=2 \\ \sqrt[3]{18}=2 \\ 2.62=2 \end{gathered}[/tex]As you can observe, the solution 12 doesn't satisfy the given equation.
Therefore, the only solution is -4.Alisa walks 3.5 miles in 30 minutes. At this rate, how many miles can she walk in 45 minutes?385.7 miles5 miles386 miles5.25 miles
Given:
Alisa walks 3.5 miles in 30 minutes.
To find:
The number of miles if she walks 45 mins.
Explanation:
The unit rate for speed is,
[tex]\begin{gathered} Speed=\frac{Distance}{Time} \\ =\frac{3.5}{30} \end{gathered}[/tex]The distance covered when she walks 45mins,
[tex]\begin{gathered} Distance=Speed\times Time \\ =\frac{3.5}{30}\times45 \\ =5.25miles \end{gathered}[/tex]Final answer:
The number of miles she walks in 45mins is 5.25miles.