Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]bridget is growing seven plants for her science project. here are the heights of the plants after four weeks. what is the mode?
Given the data:
Plant Height(Cm)
1 9
2 10
3 10
4 6
5 9
6 7
7 10
The mode of a data set is the value that occurs most frequently.
From the data above, the height that occurs most frequently is 10 cm.
Therefore, the mode is 10.
ANSWER:
UsetheprimefactorsmethodtofindtheGCFof76,190,and931.
There are several ways to calculate the GCF
Let's use the Prime Factorization.
1) List the numbers in a row. As we can see, 76, 190 are both divisible by 2
So le's start dividing by the prime number 2, up to next divisible prime number as it follows:
As we can see the Greatest Common Divisor to both 76,190 and 931 is the prime number 19
Therefore, we can state the GCD of 76,190, 931 as 19
help me please im not understanding on the right side it says: to the total number of people present. Express as a simplified ratio
ANSWER
4 : 9
EXPLANATION
The total number of people present is the number of females plus the number of males:
[tex]125+100=225[/tex]The ratio of number of males to total number of people is:
[tex]\frac{100}{225}[/tex]We have to simplify this fraction. Both 100 and 225 are divisible by 5:
[tex]\begin{gathered} 100\colon5=20 \\ 225\colon5=45 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}[/tex]And then again, 20 and 45 are divisible by 5:
[tex]\begin{gathered} 20\colon5=4 \\ 45\colon5=9 \end{gathered}[/tex]Therefore:
[tex]\frac{100}{225}=\frac{20}{45}=\frac{4}{9}[/tex]We can't simplify more than that, so the ratio is 4 : 9
A parent is buying two types of chocolate truffles for the children. The oldest child likes white chocolate (W), the younger two like dark chocolate (D) and the spouse likes white chocolate (W). Four white chocolate truffles (W) cost the same as three dark chocolate truffles (D). If the parent bought 8 white chocolate truffles(W) and 10 dark chocolate truffles (D), and spent $50.00, how much was each dark chocolate truffle?2.422.343.13
SOLUTION
Given the information on the question tab;
[tex]Let\text{ the price for a white chocolate truffle be W, and the price for a dark chocolate truffle be D;}[/tex][tex]\begin{gathered} From\text{ the statements made in the question;} \\ 4W=3D-----(1) \\ 8W+10D=50----(2) \end{gathered}[/tex][tex]\begin{gathered} From\text{ equation \lparen1\rparen;} \\ W=\frac{3D}{4}-----(3) \\ substituting\text{ W=}\frac{3D}{4}\text{ into equation \lparen2\rparen} \end{gathered}[/tex][tex]\begin{gathered} 8\times\frac{3D}{4}+10D=50 \\ 6D+10D=50 \\ 16D=50 \\ D=\frac{50}{16} \\ D=3.125\approx3.13 \end{gathered}[/tex]Final answer:
Each dark chocolate truffle costs $3.13
find the slope of a line that is PARALLEL to y=3/5x-2
Parallel lines have the same slope.
In this case, the slope of the line is 3/5.
Then, any line that satisfies y=3/5*x+C, being C any constant, is parallel to our line.
Then, when C=0 for example, we have the line y=3/5*x that is parallel and goes through the center of coordinates (0,0).
Graphically, we can see that they a re parallel:
Answer: y = 3/5*x + C, with C=constant. There are infinte solutions if no other restriction is made, so for example y=3/5*x is parallel to y=3/5*x-2.
Use a truth table to determine whether the two statements are equivalent.
The answer is option(b) i.e,the given statements are not equivalent.
What is Truth table?
A truth table is a breakdown of a logic function by listing all possible values the function can attain. Such a table typically contains several rows and columns, with the top row representing the logical variables and combinations, in increasing complexity leading up to the final function.
Let's proof it by using truth table :
p q (~q → ~p) (~p → ~q)
F F T T
F T T F
T F F T
T T T T
As you've seen in truth table (~q → ~p) ≠ (~p → ~q)
Therefore, the answer is option(b) i.e,the given statements are not equivalent.
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What is the volume of the cone rounded to the nearest tenth? The diagram is not drawn to scale. The height of the cone is 19 yd.A) 2646.3 yd^3B) 1462.4 yd^3C) 1039.0 yd^3D) 975.0 yd^3
Answer:
To find the volume of the cone rounded to the nearest tenth
we have that,
Volume of the cone (V) is,
[tex]\frac{1}{3}\pi r^2h[/tex]where r is the radius and h is the height of the cone.
Given that,
r=7 yd
h=19 yd
Substitute the values we get,
[tex]V=\frac{1}{3}\pi(7)^2\times19[/tex]we get,
[tex]V=\frac{931}{3}\pi[/tex]we know that pi is approximately equal to 3.14, Substitute the value we get,
[tex]V=\frac{931}{3}(3.14)[/tex]we get,
[tex]V=974.446\approx975\text{ yd}^3[/tex]Answer is: Option D:
[tex]\begin{equation*} 975\text{ yd}^3 \end{equation*}[/tex]This is due tomorrow! Smart people help me, please!!
At Bright Futures Middle School, 576 students ride their bike to school . If this number is 75% of the school enrollment, then how many students are enrolled
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
students on bike = 576
% students on bike = 75%
total students = ?
Step 02:
total students
[tex]\text{ \% students on bike = }\frac{students\text{ on bike }}{\text{total students }}\cdot100[/tex][tex]\begin{gathered} 75\text{ = }\frac{576}{\text{total students }}\cdot100 \\ \text{total students = }\frac{576}{75}\cdot100 \end{gathered}[/tex]total students = 768
The answer is:
The number of total students is 768.
Nadine tried to solve the equation 12x - 19 equals -4 (3 x - 9) - 15 but made a mistake which line shows evidence of Nadines mistake
Answer:
Line 4
Explanation:
The initial expression is:
12x - 19 = -4(3x - 9) - 15
The mistake was made on line 4, the correct steps to solve the expression are:
[tex]\begin{gathered} 12x-19=-4(3x-9)-15 \\ 12x-19=-12x+36-15 \\ 12x-19=-12x+21 \\ 24x-19=21 \\ 24x-19\textcolor{#FF7968}{+19}=21\textcolor{#FF7968}{+19} \\ \textcolor{#FF7968}{24x=40} \\ x=\frac{40}{24}=\frac{5}{3} \end{gathered}[/tex]Because on line 4 they subtract 19 from the right side and the correct step is to add 19 to the right side.
Solve for the triangle where there is a question mark!
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Label the right-angled triangle
STEP 2: Write the trigonometry ratios
[tex]\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \\ \tan \theta=\frac{\text{opposite}}{\text{adjacent}} \end{gathered}[/tex]STEP 3: Write the given values to decide which ratio to use
Let the part with the question be represented by m
[tex]\begin{gathered} \text{adjacent}=7,\text{hypotenuse}=12,m=\text{?} \\ U\sin g\text{ the cos ratio from step 2;} \\ \cos m=\frac{7}{12} \\ m=\cos ^{-1}(\frac{7}{12})=\cos ^{-1}0.5833333333 \\ m=54.31466529 \\ m\approx54.31 \end{gathered}[/tex]Therefore, the value of mising angle labelled m is approximately 54.31 degrees
What is the vertical shift for the absolute value function below?f(x) = 9|x + 11 + 2
Since the function is shifted 2 units up, the vertical shift is 2
A circle and two distinct lines are drawn on a sheet of paper what is the largest possible number of points of intersection of these figures (it is Q29)
Answer:
C 5
Step-by-step explanation:
The two lines can both intersect the circle twice, and can intersect each other once, so 2 + 2 + 1 = 5
Use the parabola tool to graph the quadratic function f(1) = 2x^2+16x+30Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
vertex(-4,-2)
focus(-4,-15/8)
Axis of symmetry,x=-4
directrix, y=-17/8
x y
-6 6
-5 0
-4 -2
-3 0
-2 6
43% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor theuse of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight(a) P(3) =(Round to three decimal places as needed.)
EXPLANATION:
According to the established pattern that only 43 out of 100 adults favor the use of drones, now we must find out from the only twelve adults surveyed how much corresponds to 43 percent.
The first thing we must do is make the relation 12 equals 100, then 43 percent how much?
[tex]\begin{gathered} 12\rightarrow100 \\ x\leftarrow43 \\ x=\frac{12\times43}{100} \\ \textcolor{#FF7968}{x=5.16}\text{\textcolor{#FF7968}{ ; }} \\ \text{the answer is }\text{\textcolor{#FF7968}{5.16 }}\textcolor{#FF7968}{that}\text{\textcolor{#FF7968}{ is less than eight }}\text{; } \end{gathered}[/tex]A container of orange juice cost $3.29 for 59 ounces. What is the unit rate to the nearest penny?
Answer:
6 cents
A colony of 4,050 bacteria doubles in size every 297 hours. What will the population be 594 hours from now?
Answer:
About 280,000
Step-by-step explanation:
Answer:
16,200
Step-by-step explanation:
594 ÷ 297 = 2
4,050 × 2 × 2 = 16,200
another way: 4,050 × 2^2 = 16,200
3. Carlos Quintero, Treasurer of X Corp is analyzing an investment on two projects, C and D. The data to
consider are shown below
Initial Investment
Annual Rate of
Return
Pessimistic
Most Likely
Optimistic
Amount
$135,000
39%
27%
25%
Project C
Probability
.30
.45
.25
Amount
$145,000
25%
15%
30%
Project D
Probability
.35
.40
.25
A. Determine the rates of return for each of the two projects. (6 points)
The rates of return for each of the two projects for X Corp are as follows:
Project C = 30.1%Project D = 19.75%.What is the rate of return?The rate of return refers to the percentage gain or loss over the initial cost of the investment.
For this purpose, the rate of return is expressed as the percentage of the expected returns (which is a product based on the probability of different scenarios) over the initial investment cost.
Project C Project D
Amount Probability Amount Probability
Initial Investment $135,000 $145,000
Annual Rate of Return
Pessimistic 39% .30 25% .35
Most Likely 27% .45 15% .40
Optimistic 25% .25 30% .25
Returns from Project C:Pessimistic $15,795 ($135,000 x 39% x 30%)
Most likely $16,402.50 ($135,000 x 27% x 45%)
Optimistic $8,437.50 ($135,000 x 25% x 25%)
Total expected returns = $40,635
Rate of return = 30.1% ($40,635/$135,000 x 100)
Returns from Project D:Pessimistic $9,062.50 ($145,000 x 25% x 35%)
Most Likely $8,700 ($145,000 x 15% x 40%)
Optimistic $10,875 ($145,000 x 30% x 25%)
Total expected returns = $28,637.50
Rate of return = 19.75% ($28,637.50/$145,000 x 100)
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Completely the instructions to move from one point to another along the line y = 2/3x+1. Down 4 units then. Units.
The parent function given is,
[tex]y=\frac{2}{3}x+1[/tex]We were told the parent function was translated 4 units down, which means
[tex]\begin{gathered} y=\frac{2}{3}x+(1-4) \\ y=\frac{2}{3}x-3 \end{gathered}[/tex]Hence, the transformed function would be,
[tex]y=\frac{2}{3}x-3[/tex]Let us now plot the graph of the parent function and the transformed function in order to compare the two graphs.
From the graph above, the parent function is represented in the green line while the transformed function is represented in the black line.
Therefore, the answer is
Down 4 units, then left 6 units.
what are the reasons ? and is there anymore statements
The first reason is GIVEN
If angles ∠XWY and ∠RTU are supplemetary, it means they add up 180°. It demands that lines It demands that lines It demands that
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of
producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile
is given by R(x)=230x. Find the break-even point and the cost and revenue at the break-even point.
The break-even point is
The cost at the break-even point is $
The revenue at the break-even point is
units.
www
The break-even point=30, The cost of producing x units of tile =6900$, revenue from the sale of x units of tile at the break-even point=6900$.
What is equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What is revenue?Revenue is the total amount of money made from the sale of products and services that are essential to the business's core operations. Sales or turnover are other terms used to describe commercial revenue. Some businesses make money from royalties, interest, or other fees.
The manager of a small company that produces roof tile has determined that the total cost in dollars, C(x), of producing x units of tile is given by C(x) = 200x + 900, while the revenue in dollars, R(x), from the sale of x units of tile is given by R(x)=230x.
C(x) = 200x + 900
R(x)=230x
200x+900=230x
30x=900
x=30
C(x)=200*30+900
=6900
R(x)=230*30=6900
30 is the break-even point; At the break-even point, the cost of producing 30 units of tile is $6900, and the revenue from those sales is $6900.
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y - 32 = -2(x-48)what is y
y - 32 = -2( x - 48)
y - 32 = -2x + 96
y = -2x + 96 + 32
y = -2x + 128
Lars created a painting with an area of 42 square inches and a length of 6 inches. They create a second painting with an area of 28 square inches. It has the same width as the first painting. What is the length of the second painting?
The length of the second painting is 4 in.
What is Area of Rectangle?
Area of rectangle is length times of breadth.
Given that :
Lars created a painting with an area of 42 square inches and a length of 6 inches. now, calculating B of painting using formula :
Area of Rectangle=Length × Width
42 = 6 x b
b = 42/6
b = 8 in.
it is given that :
area of second painting = 28 square inches
and having same width as the first painting that is b = 8 in.
Now, calculating length second of painting using formula :
Area of Rectangle=Length × Width
28 = l x 8
l = 28/8
l = 4 in.
Therefore, the length of the second painting is 4 in.
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Mick O'Meara budgeted $315 per month for electricity and $238 per month for gas. His expenses for a twelve-month period were $3,950 for electricity and $3,055 for gas.How much less did he budget annually for the two expenses than he needed?$339$344$357$369None of these choices are correct.
In order to know how much he budgeted annually for each expense, we need to multiply each month budget by 12:
annual budget for electricity: 12 * 315 = 3780
annual budget for gas: 12 * 238 = 2856
So, the total annual budget was:
3780 + 2856 = 6636
On the other hand, his real expenses for that year were:
3950 + 3055 = 7005
Then, to find how much less he budget than he needed, we can find the difference between those two values:
7005 - 6636 = 369
Therefore, the last option is correct.
URGENT TWO WAY TABLES
Answer: A) 6 B) 19.5
Step-by-step explanation:
A) 2,4,6,8,10
B) 8+16+30+24=78
78/4=19.5
Let me known if question b was right
b. 9m2 + 6m + 6 = 5 has real roots and imaginary roots
the given equation is
[tex]\begin{gathered} 9m^2+6m+6=5 \\ 9m^2+6m+1=0 \end{gathered}[/tex]we will calculate
[tex]D=b^2-4ac[/tex]so
[tex]\begin{gathered} =6^2-4\times9\times1 \\ =36-36 \\ =0 \end{gathered}[/tex]as D is 0 so it has one real root
if Dixon is 6 ft tall,, how tall is ariadne?
Notice that the triangles formed by the shadows are similar, therefore:
[tex]\frac{x}{6}=\frac{15}{18},[/tex]where x is Adriadne's height. ( We will omit the units to simplify the calculations).
Solving the above equation for x, we get:
[tex]x=\frac{15}{18}*6.[/tex]Simplifying the above result, we get:
[tex]x=5ft.[/tex]Answer:[tex]5ft.[/tex]
andrews family spent 410 on 2 adult tickets to go to the concert. maxs family spent 375 on 3 tickets and 2 child tickets 3 how much is the adult ticket how much is a child ticket
Let 'x' represents the cost of the ticket for an adult, and 'y' be the cost of a child's ticket.
Andrew's family spend 410 on two adult tickets.
[tex]2x=410[/tex]From the above expression,
[tex]\begin{gathered} x=\frac{410}{2} \\ =205 \end{gathered}[/tex]Thus, the cost of an adult ticket is 205.
Given that the Max's family spend 375 for 3 tickes, and two of them is for childrens.
[tex]\begin{gathered} x+2y=375 \\ 205+2y=375 \\ 2y=375-205 \\ 2y=170 \\ y=\frac{170}{2} \\ y=85 \end{gathered}[/tex]Thus, the cost for tickets for the childrens is 85.
Trey's chocolate bar is 52% cocoa. If the weight of the chocolate bar is 66 grams, how many grams of cocoa does it contain? Round your answer to the nearest
tenth.
Trey's chocolate bar is 52% cocoa and if the weight of the chocolate bar is 66 grams, it contains 34.32 grams of cocoa using the concept of percentage.
What is percent?A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement.What is a fraction?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many parts of a particular size there are when spoken in everyday English.Here, 52% of 66 grams:
=(52/100)*66=0.52*66=34.32 grams of cocoa52% cocoa makes up Trey's chocolate bar.
Using the concept of percentage, a 66-gram chocolate bar would contain 34.32 grams of cocoa.
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In a data set, the median is less than the mean. What does that indicate about the data?A.It is skewed to the right.B.It is skewed to the left.C.It is symmetric.D.It is bell-shaped.
SOLUTION:
Step 1:
In this question, we are given the following:
In a data set, the median is less than the mean. What does that indicate about the data?
A. It is skewed to the right.
B. It is skewed to the left.
C. It is symmetric.
D. It is bell-shaped.
Step 2:
The diagram that explains the question above is:
A left-skewed distribution has a long left tail. Left-skewed distributions are also called negatively-skewed distributions. That’s because there is a long tail in the negative direction on the number line. The mean is also to the left of the peak.
A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.
Back to the question, in a data set, the median is less than the mean
It indicates that:
It is skewed to the right ( OPTION A )