By using 3 factors 2, 3, and 7, if we create a product game board with the numbers 4 6 9 14 49 then the missing product is 21.
To solve this problem we have to follow a few steps. First, we should know about factors.
What are the factors?
Factors of a number are such numbers as they can divide the whole number without remaining.
Example: The factors of 24 are 1, 2, 3, 4, 6, 8, and 12.
Now we have to analyze the given numbers,
4 = 2× 2
6 = 2× 3
9 = 3× 3
14 = 2× 7
49 = 7× 7
The factors are 2, 3, and 7. Therefore, the missing product is, 3× 7= 21
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What is the logarithm of
6.5
The logarithm of the number 6.5 is log(6.5) = 0.8129
What is the logarithm of numbers?This is the number that represents the power by which a fixed number known as the base must be raised to result in another number.
How to evaluate the logarithm of the number?The number is given as
6.5
The logarithm of the number is then represented as
log(6.5)
There are several ways to calculate the logarithm of the number
Some of which are:
By logarithm tableBy calculatorIn this case, the only way is by using a calculator
Using a calculator, we have
log(6.5) = 0.8129
Hence, the logarithm of 6.5 is 0.8129
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65% of the workers at Costco have a pet dog. If thereare about 162 workers who have a dog, how manyCostco employees are there in total? .
To find how many Costco employees are, we can use the formula of
Atoms can’t ever be _ or _ in a chemical reaction. the atoms must always be _ each side of the equation
In a chemical reaction, atoms are neither CREATED nor DESTRUCTED. According to science, each side of the equation must contain the SAME amount of atoms.
You must place COEFFICIENTS in front of the chemical formulas in the equation in order to make it equal.
What does a chemical reaction always involve?
Only atoms from the reactants can end up in the products of a chemical reaction. No atoms are destroyed or made into new ones. When reactants come into touch with one another, the bonds between their atoms are broken, and the atoms then reorganize and form new bonds to create the products.
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A rectangular calendar is hanging on a wall. The diagram below shows several dimensions of the wall and the calendar.Based on the diagram, determine the distance that the top edge of the calendar is from the ceiling, and explain your reasoning.
SOLUTION
We want to find the distance that the top edge of the calendar is from the ceiling.
The diagram below will help us
From the diagram above x is the distance we want to find
We can see that the entire wall is 9 ft long,
Distance from the foot of the calender to the floor is 5 1/4 ft and
Halve of the calendar is 2/3 ft
So the whole calendar is
[tex]\begin{gathered} 2\times\frac{2}{3} \\ =\frac{4}{3}\text{ ft } \end{gathered}[/tex]So, to find x, we will add length of the calendar which is 4/3 ft to distance from the foot of the calender to the floor which is 5 1/4 ft and subtract this from height of the wall which is 9 ft
We have
[tex]\begin{gathered} 9-(\frac{4}{3}+5\frac{1}{4}) \\ 9-(\frac{4}{3}+\frac{21}{4}) \\ 9-(\frac{16+63}{12}) \\ 9-\frac{79}{12} \\ =\frac{108-79}{12} \\ =\frac{29}{12} \\ =2\frac{5}{12} \end{gathered}[/tex]Hence the answer is
[tex]2\frac{5}{12}\text{ ft}[/tex]find the surface area of the figure in square inches.
The surface area of a cone is given by the sum of the areas of the lateral surface and the area of the circular base.
The area of the circular base is given by:
[tex]\pi\cdot r^2[/tex]Where r is the radius of the base.
The area of the lateral surface is given by:
[tex]\pi rs[/tex]Where s is the length of the slant.
Since s=17 in and the radius is half the diameter, r=8 in, the area of the cone is:
[tex]\begin{gathered} A=\pi rs+\pi r^2 \\ =\pi(8)(17)+\pi(8)^2 \\ =136\pi+64\pi \\ =200\pi \\ =628.3185307\ldots \end{gathered}[/tex]To the nearest hundredth, the area of the cone in square inches, is:
[tex]628.32[/tex]This year for Spring break you are taking a solo trip to an exotic destination. You are deciding between two destinations: Bali, Indonesia, and Paris, France. You want to choose the destination that will give you the best value for your money.The table below shows the cost to travel to each destination Flight Hotel (pernight)Bali $967 $58Paris $534 $2551. Create an equation for each destination to represent cost, C to travel to that location based on n Number of nights.
Let n represent the number of nights
Cost to travel to Bali:
[tex]C\text{ = 967 + 58n}[/tex]The cost of flight is constant so we simply add it to the cost of hostel per night times the number of nights
Cost to travel to Paris:
[tex]C\text{ = 534 + 255n}[/tex]hello can you help me solve this plane trigonometry question
Problem
Solution
For this case we can find the remain angle with this operation:
180 -39-90= 51º
And then we can use the sines law and we can do this:
[tex]\frac{x}{\sin(39)}=\frac{14}{\sin (90)}[/tex]And solving for x we got:
x= 14*sin(39)/sin (90) = 14*sin 39= 8.81
define the domain of the following:
By identifying the first values of each point in the graph, we saw that the domain of the relationship is:
D: {-3, -1, 1, 3, 6}
How to get the domain?A relation can be defined by a set of points (x, y), where the values of x are the values in the domain and the values of y are the values in the range.
Here we have the graph of a relation, and we can see the points:
(-3, 3)(-1, -1)(1, 2)(3, 0)(6, -2)
The domain of the graphed relationship will be the set of the first values of each of these points, then we can see that the domain is:
D: {-3, -1, 1, 3, 6}
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write from largest to smallest these numbers 5/4,.2,60%,.75,.5
Find the critical value (tα/2) for a 95% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
The critical value (tα/2) for a 95% confidence interval for the sample size 15 is 2.009.
We have to find the critical value tα/2 for 95% confidence interval, we are given the sample size.
First we will find the alpha value to get the critical value.
=100%-95%
=1-0.95
=0.05
α=0.05
α/2=0.05/2
α/2=0.025
degrees of freedom(df)= n-1=15-1=14
We will use degrees of freedom and α/2 values to find the critical value that is tα/2.
By using the t table we get the critical value of tα/2=2.009.
Therefore, the critical value for 95% confidence interval with sample size of 15 is 2.009.
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Assume that a procedure yields a binomial distribution with a trial repeated n = 5 times. Use some form of technology to find the probability distribution given the probability p = 0.82 of success on a single trial.
Answers in bold
[tex]\begin{array}{|c|c|} \cline{1-2}k & P(X = k)\\\cline{1-2}0 & \boldsymbol{0}\\\cline{1-2}1 & \boldsymbol{0}\\\cline{1-2}2 & \boldsymbol{0.04}\\\cline{1-2}3 & \boldsymbol{0.18}\\\cline{1-2}4 & \boldsymbol{0.41}\\\cline{1-2}5 & \boldsymbol{0.37}\\\cline{1-2}\end{array}[/tex]
Note: The P(x) values for k = 0 and k = 1 are not actually zero, but they are small enough that they round to 0 when rounding to two decimal places.
=======================================================
Explanation:
I used a spreadsheet to compute the values in bold.
The specific command is called BINOMDIST
The template is BINOMDIST(k,n,p,0)
k = value from the tablen = 5p = 0.82The 0 at the end tells us to use a binomial PDF and not CDFLet me know if you have any questions about how to use that function in a spreadsheet.
Also, I used the function called ROUND to round each value to 2 decimal places.
Example calculation
=ROUND(BINOMDIST(4,5,0.82,0),2)
This calculates the result of 0.41 and it corresponds to the value k = 4
Don't forget about the equal sign up front when computing these commands in the spreadsheet. Otherwise, it'll stay as text form.
-------------------
If you want to use a TI83 or TI84 calculator, then press the button labeled "2nd". Then press the button labeled "VARS". Scroll down until you reach "binompdf".
The template is binompdf(n,p,k)
So for example, type in binompdf(5,0.82,4) to get the P(X) value for k = 4
If you aren't able to access a spreadsheet or a TI83/84 calculator, then search out "binomial distribution calculator" and there are plenty of free ones to pick from.
In my opinion, a spreadsheet is the best option since the given data is already in tabular form. Also, many real world situations and careers use spreadsheets everyday.
Find the surface area of the net.Enter the correct answer in the box.
We can divide the given figure into different rectangular faces:
Faces 1 and 3 have the same measure, also 2 and 4, and faces 5 and 6.
Faces 1 and 3 have the following dimensions: L=100cm W=50cm.
Faces 2 and 4 have the following dimensions: L=100cm W=35cm.
Faces 5 and 6 have the following dimensions: L=50cm W=35cm.
The surface area of a rectangular face is given by:
[tex]SA=L*W[/tex]Thus, the surface areas of the given faces are:
[tex]\begin{gathered} SA_1=100cm*50cm=5000cm^2 \\ SA_3=100cm*50cm=5000cm^2 \\ SA_2=100cm*35cm=3500cm^2 \\ SA_4=100cm*35cm=3500cm^2 \\ SA_5=50cm*35cm=1750cm^2 \\ SA_6=50cm*35cm=1750cm^2 \end{gathered}[/tex]The surface area of the net is the addition of all of these surface areas:
[tex]\begin{gathered} SA_{net}=(5000+5000+3500+3500+1750+1750)cm^2 \\ SA_{net}=20500cm^2 \end{gathered}[/tex]Identify the translation of the vertices P (-4, -5), L (1, -7), and K (-9, 8), along the vector , <-6 , 3 >.
Given:
The vertices are P (-4, -5), L (1, -7), and K (-9, 8).
The vector is < -6,3 >.
Aim:
We need to find the image of the vertices when translating given vertices along the vector.
Explanation:
The translation vector <-6,3> means each point is being moved 6 units to the left and 3 units up.
For each vertex, we subtract 6 from each x value and add 3 to each y value.
[tex]P^{\prime}(-4-6,-5+3)=P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(1-6,-7+3)=L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-9-6,8+3)=K^{\prime}(-15,11)[/tex]Final answer:
[tex]P^{\prime}(-10,-2)[/tex][tex]L^{\prime}(-5,-4)[/tex][tex]K^{\prime}(-15,11)[/tex]
Abigail wants to find three consecutive even integers whose sum is four times the smallest of those integers. She lets n represent the smallest integer, then writes this equation: n + (n + 2) + (n + 4) = 4n. What are the three integers?
The three consecutive integers according to the expression will be 6, 8, 10
In the given question, there is an expression stated that tells the condition for a sequence in which a number is represented by 'n'. The expression is the sum of three even integers whose sum is equal to four times the smallest of numbers.
The expression is n + (n + 2) + (n + 4) = 4n. We have to find out the values for each of the numbers.
Here, First Number = n
Second number = (n + 2)
Third Number = (n + 4)
Now, We will calculate the given expression to find out the value of n.
=> n + (n + 2) + (n + 4) = 4n
=> 3n + 6 = 4n
=> n = 6
We get the smallest number n = 6 which is the first number, the second number is 8, and the third number is 10.
Hence, the numbers are 6, 8, and 10.
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how many meters are in 11.75 millimeters
ANSWER
0.01175 metres
EXPLANATION
We want to find how many metres are in 11.75 millimetres.
There are 1000 millimeters in 1 meter:
We will simply divide 11.75 milimetres by 1000
1000 millimetres = 1 metre
[tex]11.75\text{ millimetres = }\frac{11.75}{1000}\text{ = 0.01175 metres}[/tex]what is zero divided by zero
Answer:
indetermination
Step-by-step explanation:
Hope this helps
Find the midpoint M of the line segment joining the points
Given,
The coordinates of the points is,
[tex](-4,5)\text{ and \lparen2,-1\rparen}[/tex]The coordinates of the mid point is:
[tex]\begin{gathered} Consider,\text{ x and y are the coordinates of the midpoint} \\ x=\frac{-4+2}{2}=-\frac{2}{2}=-1 \\ y=\frac{5-1}{2}=\frac{4}{2}=2 \\ \end{gathered}[/tex]Hence, the mid point of the line segment is (-1,2).
pls answer the pic below
The value of the missing angles are; m∠ABC = 36° and m∠DBC = 41°
How to find the missing angles?We are given that;
m∠ABD = 77°
Addition angle postulate states that the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together.
Now, by addition angle postulate, we can say that;
m∠ABC + m∠DBC = 77°
Now, we are given that;
m∠ABC = (5x - 4)°
m∠DBC = (5x + 1)°
Thus, by substitution property, we have;
(5x - 4)° + (5x + 1)° = 77
10x - 3 = 77
10x = 77 + 3
10x = 80
x = 8
Thus;
m∠ABC = (5(8) - 4)°
m∠ABC = 36°
m∠DBC = (5(8) + 1)°
m∠DBC = 41°
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Assume that a sample is used to estimate a population proportion p. Find the 95% confidence interval for a sample of size 318 with 57% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.
A population proportion's 95% confidence interval is 0.45416 ≤ P ≤ 0.66584.
Given sample size n is 318, the probability of success,
p = x ÷ n = 181 ÷ 318 = 0.56
A population proportion's 95% confidence interval is calculated as follows:
(p - [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n) , p + [tex]Z_{0.05}[/tex] √(p(1 - p) ÷ n)
(0.56 - 1.96 √ ((0.56(1 - 0.56) ÷ 318) , 0.56 + 1.96 √ ((0.56(1 - 0.56) ÷ 318))
(0.56 - 1.96 × 0.054) , (0.56 + 1.96 × 0.054)
(0.45416 , 0.66584)
95% confidence interval for a population proportion of 0.45416 ≤ P ≤ 0.66584.
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what is (9.74c-250.50)+(-5.48p+185.70)
Here, we want to solve find the value of the expression
We start by opening up the brackets and then, we bring together like terms
We have this as;
[tex]\begin{gathered} (9.74c-250.5)+(-5.48p+185.70) \\ =\text{ 9.74c - 250.5 -5.48p+185.7} \\ =\text{ 9.74c-5.48p-250.5+185.7} \\ =\text{ 9.74c-5.48p-64.80} \end{gathered}[/tex]500/675x9876=? what is the answer ???????????
Answer:
7315.55
Step-by-step explanation:
just dont be lazy solve it.
1. Which statement is true? (1 point)
29 20
35
18
34
14
A
A
30
16
32
17
>
21 24
20 28
15
23
Fraction - A,C,D is the incorrect option that means 18 >17 is the correct option B
What does compare mean in fractions?Equivalent fractions with the same denominator should be used to compare fractions with different denominators. Comparing fractions: If the denominators are the same, the numerators can be compared. The greater fraction is the one with a larger numerator.
Now, comparing the fraction,
first of all write the fraction in simplest form then cross multiplication.
1. [tex]\frac{29}{35} < \frac{20}{30}[/tex]
[tex]\frac{29}{35} < \frac{2}{3}[/tex]
87 < 70
This option is wrong.
2. [tex]\frac{18}{34} > \frac{16}{32}[/tex]
[tex]\frac{9}{17} > \frac{1}{2}[/tex]
18 >17
This option is correct.
3. [tex]\frac{14}{21} > \frac{17}{24}[/tex]
[tex]\frac{2}{3} > \frac{17}{24}[/tex]
48 > 51
This option is wrong.
4. [tex]\frac{20}{15} < \frac{28}{23}[/tex]
[tex]\frac{4}{3} < \frac{28}{23}[/tex]
92 < 84
This option is wrong.
Hence, option b is correct.
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at what point does the like given by the following equation cross the y axis? y=(-5/7)x+5A.(0,-5/7)B.(5,0)C.(0,5)D.(0.-25/7)
Given:
Given the equation
[tex]y=-\frac{5}{7}x+5[/tex]Required: Point at which the equation crosses the y axis.
Explanation:
At y -axis, the value of x is zero. Substitute 0 for x in the equation of y.
[tex]\begin{gathered} y=-\frac{5}{7}\cdot0+5 \\ =0+5 \\ =5 \end{gathered}[/tex]So, the point at which the equation cross the y-axis is (0, 5).
Final Answer: The point at which the equation cross the y-axis is (0, 5).
The following are the reasons why sampling is used except for a. Sampling is used if taking a census of the entire population is impractical. b. Sampling is less time-consuming and less costly than census. c. Sampling is so easy. d. The data from the sampling can be used to estimate corresponding population measures.
The following are the reasons for sampling:
1. To bring the population to a manageable number
2. To reduce cost
3. To help in minimizing error from the despondence due to large number in the population
4. Sampling helps the researcher to meetup with the challenge of time.
Therefore, the answer is:
c. Sampling is so easy.
2) In reply to an inquiry about the animals on his farm, the farmer says: "I
only ever keep sheep, goats, and horses. In fact, at the moment they are
all sheep bar three, all goats bar four, and all horses bar five." How many
does he have of each animal?
The number of horse is 1, goat is 2 and sheep is 3 a man has.
The problem we are dealing with is related to the linear equation which is referred to as the algebraic condition where each term has an exponent of 1 and when this condition is graphed, it continuously comes about in a straight line.
Now w consider x to be the number of sheep, y to be the number of goats, and z to be the number of horses the man owns.
the actual equation for the total number of animals he owns is :
x+ y+ z
according to the first condition:
that all sheep bar three, means
y+ z=3
similarly, for the other condition, it will be
x+ z=4 and x+ y=5
Now we adding the three equations:
y + z +x +z +x +y=5+4 +3
2(x+y+z)=12
x+y+z=6........equation(1)
As x + y = 5
Put this in equation in (1), we get
x+y+z = 6
5 + z = 6
z = 1
x + z = 4
x + y + z = 6
y + 4 = 6
y = 2
Now we know
x + y + z = 6
x + 1 + 1 = 6
x = 4
So simplifying the other equation we get, that the number of horse is 1, goat is 2, and sheep is 4.
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Write a function that models the population of 400 birds decreased at an annual rate of 6%
A function that models the population of 400 birds decreasing at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex] where t is the time period.
What is the Exponential decay formula?The Exponential decay formula aids in determining the quick decrease over time, i.e. the exponential decrease. The exponential decay formula is used to calculate population decay, half-life, radioactivity decay, and so on.
Its general form is f(x) = a (1 - r)ⁿ.
Where a = the initial amount
1 - r = decay factor and n = time period.
Given:
The initial population of birds, P = 400
Rate of decay, r = 6% = 0.06
Time = t years
By using the exponential decay formula,we get
[tex]f(x) = P (1 - r)^{t}[/tex]
[tex]f(x) = 400(1 - 0.06)^{t}[/tex]
Therefore, the function that models the population of 400 birds decreased at an annual rate of 6% is [tex]f(x) = 400(1 - 0.06)^{t}[/tex].
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HELP ME OUT PLEASE!!!!!!!
What is the solution to the system?
Answer:
(-7, 5) is correct.
Step-by-step explanation:
[tex]2x + 3y = 1[/tex]
[tex] - 2x - y = 9[/tex]
Add these two equations, and then solve for y.
[tex]2y = 10[/tex]
[tex]y = 5[/tex]
Substitute this value of y into 2x + 3y = 1, and solve for x.
[tex]2x + 3(5) = 1[/tex]
[tex]2x + 15 = 1[/tex]
[tex]2x = - 14[/tex]
[tex]x = - 7[/tex]
So (-7, 5) is the correct solution.
please help me solve part 3!
Step-by-step explanation:
probabilities are always
desired cases / totally possible cases
24 cans in total, 4 of them are diet, therefore 20 of them are regular.
2 cans are picked.
for the first can
the probability to pick a diet can is
4/24 = 1/6
the probability to pick a regular is
20/24 = 5/6
a)
to pick 2 diets, the first one has to be diet.
that leaves 23 cans with 3 being diet.
so, the probability for the second can being diet too is
3/23.
as combined event the probability to pull 2 diet cans is
1/6 × 3/23 = 1/2 × 1/23 = 1/46 = 0.02173913...
≈ 0.0217
b)
now the same for picking 2 regular cans.
the first one has to be regular :
5/6
that leaves for the second one 23 cans and 19 of them regular
19/23
combined this gives the probability
5/6 × 19/23 = 95/138 = 0.688405797...
≈ 0.6884
this is not unusual.
what would be considered "usual" or "unusual" ?
c)
one of them is diet, and one of them is regular.
the simple answer ?
it is the only other option, when the cans are not of the same type. it is the opposite of the sum of a) and b).
so, it is
1 - 0.688405797... - 0.02173913 = 0.289855072...
≈ 0.2899
but what to do, if we want to calculate it directly ?
it is the case that either
1. the first can is diet and the second can is regular,
or
2. the first can is regular and the second can is diet.
case 1.
the first can is diet = 1/6
leaving 23 cans with 20 being regular
the second can being regular = 20/23
together
1/6 × 20/23 = 1/3 × 10/23 = 10/69 = 0.144927536...
case 2.
the first can is regular = 5/6
leaving 23 cans with 4 diets.
the second can being diet = 4/23
together
5/6 × 4/23 = 5/3 × 2/23 = 10/69 = 0.144927536...
in an "exclusive or" situation we can add the probabilities.
so, the probability of having exactly one can diet and exactly one can regular is
0.144927536... + 0.144927536... = 0.289855072...
≈ 0.2899
we were correct in the first place !
JohanVanDeVaseYesterdayMathematicsHigh SchoolTARIFF SYSTEMSQUESTION 1 [13 marks]A shopping mall in Bloemfontein has several parking garages, each with its own tariff system. The table below shows the tariffs on garage A and garage B.(Please show calculation)Parking TariffsNumber of hours (h)0 < h < 11 < h < 22 < h < 44 < h < 66 < h < 7h > 7Garage AFreeR5,50R15,50R30,50R50,50R75,50Garage BR5,00R7,00R11,00R26,00R41,00R61,00Question 1.1 [4 marks]Sellwane works at the shopping mall. She arrives at 7:30 and leaves at 17:00 each day. Which parking garage is cheaper for her to use?Question 1.2 [3 marks]Isaac was having coffee with his friends at a restaurant at the shopping mall. They arrived at the mall at 8:23 and left at 10:53, how much would he pay if he used garage B?Question 1.3 [2 marks]On Monday morning Karabo parked her car in one of the parking garages and paid R26,00. In which garage did she park and for how long?
Step 1:
Question 1.1
Arrive time = 7:30
Departure time = 17:00
[tex]\text{Total time spent = 17:00 - 7:30 = }9\colon30[/tex]h (9:30) > 7
Garage B is cheaper
Question 1.2
Arrive time = 8:23
Departure time = 10:53
[tex]\text{Total time spent = 10:53 - 8:23 = 2: 30}[/tex]The time spent by issac and his friends is between 2 < h < 4
Since h = 2:30
Answer R11.00
Question 1.3
Karabo uses Garage B
Time spent is 4 < h < 6
a) The perimeter is ____. Include units.b) The area is ___. include units.Another question is: Fully Simplify the following equation: (3x + 7) (5x^2 + 4x +9)
The perimeter is 54 inches
The area is 108 square inches
Explanation:The perimeter of the triangle is:
15 in + 15 in + 24 in
= 54 in
The area is:
(1/2)(24)(9)
= 108 sq. in