au = -10 + 4(11 - 1)
Ok
The first term is -10
What is the common difference (11 - 1)
What term are you calculating? 11 - (-10) = 11 + 10 = 21
Ringo has $100 in the bank and is adding $50 each week in savings. George has $250 in the bank, and is adding $40 each week in savings. Their plan is to wait until their savings are equal and then buy a Magic Yellow Bus and take a road trip. They figure out that the equation can be written as 50W + 100 = 40w + 250, where w is the number of weeks. How long will it take for their savings to be equal?
Answer: 15 weeks
Ringo has $100 in the bank and is adding $50 each week
Total savings for Ringo = s
s = 100 + 50 x number of weeks
Let the number of weeks = w
s = 100 + 50w ---------- equation 1
George has $250 in the bank and is adding $40 each week
s = 250 + 40 * w
s = 250 + 40w --------------- equation 2
To calculate the number of weeks that will make their savings equal, we need to equate equation 1 and 2
100 + 50w = 250 + 40w
Collect the like terms
100 - 250 = 40w - 50w
-150 = -10w
-10w = -150
Divide both sides by -10
-10w/-10 = -150/-10
w = 15 weeks
Therefore, it will take 15 weeks for their savings to be equal
In 2020, 51.3% of voters voted for Joe Biden. There were a total of 158,418,955 votes cast.a) How many people voted for Biden?
Given:
In 2020, 51.3% of voters voted for Joe Biden. There were a total of 158,418,955 votes cast.
To find: How many people voted for Biden?
Explanation:
The total number of voters = 158418955.
51.3% of voters voted for Joe Biden.
[tex]The\text{ number of people who voted for biden}=51.3\text{ \% }\times\text{ the total number of voters}[/tex]Therefore,
[tex]\begin{gathered} The\text{ number of people who voted for biden}=\frac{51.3}{100}\times158418955 \\ \\ The\text{ number of people who voted for biden}=51.3\times1584189.55 \\ \\ The\text{ number of people who voted for biden}=81268923.915 \end{gathered}[/tex]Thus, 81268923.915 people voted for Biden.
A total of $7000 is invested: part at 6% and the remainder at 10 %. How much is invested at each rate if the annual Interest is $520?
total interest = $520
Therefore,
let
x = amount invested in 6%
y = amount invested in 10%
[tex]\begin{gathered} x+y=7000 \\ y=7000-x \end{gathered}[/tex]Interest total
[tex]\begin{gathered} 520=\frac{x\times6\times1}{100}+\frac{y\times10\times1}{100} \\ 520=0.06x+0.1y \end{gathered}[/tex][tex]\begin{gathered} 520=0.06x+0.1(7000-x) \\ 520=0.06x+700-0.1x \\ 520-700=0.06x-0.1x \\ -180=-0.04x \\ x=\frac{-180}{-0.04} \\ x=\text{ \$4500} \end{gathered}[/tex]y = 7000 - 4500 = $2500
$4500 was invested at a 6% rate
$2500 was invested at a 10% rate
Which situation best represents the relationship between x and ypresented in the graph?An elevator starts at floor 4 and descends1 floor everysecond.Sarah had 0 bracelets and bought 1 new bracelet everyweek for 10 weeks.O 4 inches of rain fell every day for 10 days.A plant starts at 4 inches tall and grows 1 inch perweek.Help
startsThe situation best represents the relationship between x and y presented in the graph is the last situation which states that "A plant starts at 4 inches tall and grows 1 inch per week.
Here if we take 1 inch as 1 unit of the y axis of the graph and 1 week as the 1 unit of the x-axis. Then the graph of this situation will look like the given graph.
In the graph it is start from 4 unit of the y-axis and in every increase of 1 unit of x-axis leads to 1 unit increase of y-axis. Which is exactly the same situation as the growing of the plant.
4نما3С3 2 1NIn the similaritytransformation of ABCto ADEF, AABC was dilated bya scale factor of [?], reflected3 across the [ ], and movedthrough the translation [ ].ABА-7 -6 -5 -4 -3 -2-1 02.ED2-3יחדF-4A. 2B. 1/2C. 3D. 1/3
Explanation:
We are told to find the scale factor and the translation of the triangle ABC
To obtain the answer, we can follow the steps below
Step 1:
Get the dimensions of the triangle ABC and compare with triangle DEF
For ABC, the dimensions in units are
The dimensions of DEF are
We can compare similar sides to get the scale factor
[tex]\text{scale factor=}\frac{ED}{AB}=\frac{DF}{CA}=\frac{4}{2}=2[/tex]Therefore, the scale factor is 2
The triangle was reflected across the x-axis, and
moved through the translation by 2 units
(07.02 MC)Jason has two bags with 6 tiles each. The tiles in each bag are shown below:Make 6 squares. The squares are numbered sequentially from 1 to 6.Without looking, Jason draws a tile from the first bag and then a tile from the second bag. What is the probability of Jason drawing an even tile from the first bag and an even tile from the second bag? (1 point6 over 129 over 126 over 369 over 36
We need to find the probability of Jason drawing an even tile from the first bag and an even tile from the second bag.
Since the events of drawing a tile of each bag are independent, the final probability is the product of the two probabilities below:
• P1 ,= drawing an even tile from the first bag;
,• P2 ,= drawing an even tile from the second bag.
Notice that the tiles are numbered from 1 to 6. Thus, three of them are even:
[tex]2,4,6[/tex]Therefore, the probability of drawing an even tile from the first bag is 3 out of 6:
[tex]P_1=\frac{3}{6}[/tex]Since the second bag also has 6 tiles numbered from 1 to 6, the probability P2 is also 3 out of 6:
[tex]P_2=\frac{3}{6}[/tex]Therefore, the final probability is:
[tex]P_1\cdot P_2=\frac{3}{6}\cdot\frac{3}{6}=\frac{3\cdot3}{6\cdot6}=\frac{9}{36}[/tex]Answer
[tex]\frac{9}{36}[/tex]Is a square of an even number always even? In 1.2 you wrote the general term of sequences you wrote in 1.1.1-1.1.3 If a number is even, it can always be written as 2x another number Eg: 28 = 2 x 14 In symbols we write this as 2 x nor 2n Do you agree with the statement below? "A square of an even number is always even". Explain your answer
5)
5.1
Given equation is
[tex]P=n^2-n+41[/tex]Replace n=1, we get
[tex]P=1-1+41=41[/tex]We know that a number divisible by one and itself is called a prime number.
Here 41 is divisible by 1 and 41 only.
Hence 41 is a prime number.
5.2.
Substitute n=37 in the equation of P, we get
[tex]P=(37)^2-37+41[/tex][tex]P=1369-37+41[/tex][tex]P=1373[/tex]The number 1373 is divisible by one and 1373 only.
So 1373 is a prime number.
Hence if n=37, then P is a prime number.
5.3.
We need to choose three numbers greater than 38.
Let n=39 and substitute in P, we get
[tex]P=(39)^2-39+41[/tex][tex]P=1521-39+41[/tex][tex]P=1523[/tex]The number 1523 is divisible by one and 1523.
Hence 1523 is a prime number.
Let n=40 and substitute in P, we get
[tex]P=(40)^2-40+41[/tex][tex]P=1600-40+41[/tex][tex]P=1601[/tex]The number 1601 is divisible by one and 1601.
Hence 1601 is a prime number.
Let n=41 and substitute in P, we get
[tex]P=(41)^2-41+41[/tex][tex]P=1681-41+41[/tex][tex]P=1681[/tex]The number 1681 is divisible by one and 1681.
Hence 1681 is a prime number.
We get that
When n=39,40 and 41 then P is prime.
5.4)
Yes, I believe that this conjecture is true.
we have chosen n=1, n=39 0dd number, n=40 even number, and n=41 prime number then we get the prime number for P.
So this conjectures is true for any value of n.
The equation P gives the prime number.
Simple probability see photo
Sample space for rolling a standard cube:
[tex]\lbrace1;2;3;4;5;6\rbrace[/tex]Rolling a two:
[tex]p\text{ = }\frac{1}{6}[/tex]Rolling an odd number:
[tex]\begin{gathered} Odd\text{ numbers }\lbrace1;3;5\rbrace \\ p\text{ = }\frac{3}{6} \\ p\text{ = }\frac{1}{2} \end{gathered}[/tex]Rolling an even number
[tex]\begin{gathered} Even\text{ numbers \textbraceleft2;4;6\textbraceright} \\ p\text{ = }\frac{1}{2} \end{gathered}[/tex]Rolling a number greater than two:
[tex]\begin{gathered} >2\text{ \textbraceleft3;4;5;6\textbraceright} \\ p=\frac{2}{3} \end{gathered}[/tex]Rolling a number less than three
[tex]\begin{gathered} <3\text{ \textbraceleft1;2\textbraceright} \\ p\text{ = }\frac{1}{3} \end{gathered}[/tex]Rolling a two or a five:
[tex]\begin{gathered} 2\text{ or 5 } \\ p\text{ = }\frac{1}{3} \end{gathered}[/tex]Rolling a one:
[tex]p\text{ = }\frac{1}{6}[/tex]Rolling a number less than five:
[tex]\begin{gathered} <5\text{ \textbraceleft1;2;3;4\textbraceright} \\ p\text{ = }\frac{2}{3} \end{gathered}[/tex]A honeybee sitting on a tulip wanted to fly to a daffodil located 100 meters due east. Although the honeybee flew in a straight line, it mistakenly flew in a direction 5° south of east. When the bee was directly south of the daffodil, how many meters from the bee was the daffodil? Enter your answer to 2 decimal places.
Let's begin by listing out the given information:
Let the initial location of the honeybee be represented as B
Let the location of the honeybee be represented as C
Let the location of the daffodil be represented as D
[tex]\begin{gathered} BC(adjacent)=100m \\ \angle B=5^{\circ} \\ CD(opposite)=? \end{gathered}[/tex]We will calculate for CD using the Trigonometric ratio (SOHCAHTOA). We will use TOA:
[tex]\begin{gathered} Tan\theta=\frac{opposite}{adjacent}=\frac{CD}{BD} \\ \theta=5^{\circ},BD=100m \\ Tan5^{\circ}=\frac{CD}{100} \\ CD=100\cdot Tan5^{\circ} \\ CD=8.78\approx8.8 \\ CD=8.8m \end{gathered}[/tex]Find g(4a + 2) for the following polynomial.8(x) = - 3x + 14Answer8(4a + 2) =
SOLUTION
[tex]\begin{gathered} g(x)=-3x+14 \\ We\text{ want to find } \\ g(4a+2) \end{gathered}[/tex]To do this wherever you see x, put 4a + 2, we have
[tex]\begin{gathered} g(x)=-3x+14 \\ g(4a+2)=-3(4a+2)+14 \\ \text{expanding we have } \\ g(4a+2)=-12a-6+14 \\ =-12a-6+14 \\ =-12a+8 \end{gathered}[/tex]hence the answer is -12a + 8
Elida will use six different wires for a science project. The fractions represent the diameters of these wires in inches. Least to greatest
If we are to arrange them from least to greatest,
First, let's covert to equaivalent fraction
[tex]\frac{7}{16}=\frac{7\times2}{16\times2}=\frac{14}{32}[/tex][tex]\frac{1}{2}=\frac{1\times16}{2\times16}=\frac{16}{32}[/tex][tex]\frac{3}{8}=\frac{3\times4}{8\times4}=\frac{12}{32}[/tex][tex]\frac{9}{32}[/tex][tex]\frac{5}{16}=\frac{5\times2}{16\times2}=\frac{10}{32}[/tex][tex]\frac{15}{32}[/tex]When we have fractions with the same denominator, the one with the smallest/least numerator is the smallest/least
So comparing the above, we can now arrange;
9/32 , 5/16 , 3/8 , 7/16 , 15/32 , 1/2
Use the picture below to answer questions 9-12. F D D M, M to 9. Three collinear points are: A. DEB B.FE.D С. В.Е.М D. ADF
1) Collinear points are by definition, points that belong to the same line.
So, examining the picture we can state the 3 collinear points are:
b) FED
Note that these points are in the same line "j" so we can call them collinear.
During a movie, Lindsey ate 2/8 of a handful of snack mix, and Isabella ate 1/8 of a handful. How much more did Lindsey eat?
Given:
During a movie, Lindsey ate 2/8 of a handful of snack mix, and Isabella ate
1/8 of a handful.
Required:
Find how much more did Lindsey eat.
Explanation:
The amount that is eaten by Lindsey = 2/8
The amount that is eaten by Isabell = 1/8
The more amount that is eaten by Lindsey =
[tex]\begin{gathered} \frac{2}{8}-\frac{1}{8} \\ =\frac{1}{8} \\ =0.125 \end{gathered}[/tex]Final Answer:
The more amount that is eaten by Lindsey than by Isabell is 0.125.
y + 2x = 5; x = -1, 0, 3 Solve for y then find the value of y for each value of x.Uh how do I do that?
'Solve for y' means that you have to clear 'y' from the equation:
[tex]y+2x=5[/tex]Clearing 'y':
[tex]y=5-2x[/tex]Now, to find the value of 'y' for each value of 'x' you just have to replace 'x' in the expression above by each of the given values. This is:
For x = -1
[tex]y=5-(2\times(-1))[/tex][tex]y=5+2=7[/tex]When x = -1, y = 7.
For x = 0:
[tex]y=5-(2\times0)[/tex][tex]y=5-0=5[/tex]When x = 0, y = 5
For x = 3:
[tex]y=5-(2\times3)[/tex][tex]y=5-6=-1[/tex]When x = 3, y = -1
a scientist has two solutions which she has labeled solutions A and Solution B each contains salt she knows that solutions A is 30% salt and solution B is 80% salt. she wants to obtain 120 ounces of a mixture that is 60% salt how many ounces of each solution should she use
Explanation:
Let's call A the ounces of solution A and B the ounces of solution B.
If the scientist wants to obtain 120 ounces, then:
A + B = 120
On the other hand, the final mixture should be 60% salt and solution A is 30% salt and solution B is 80% salt, so:
0.6(A + B) = 0.3A + 0.8B
So, we can solve for A as:
[tex]\begin{gathered} 0.6(A+B)=0.3A+0.8B_{}_{} \\ 0.6A+0.6B=0.3A+0.8B \\ 0.6A+0.6B-0.3A=0.3A+0.8B-0.3B \\ 0.3A+0.6B=0.8B \\ 0.3A+0.6B-0.6B=0.8B-0.6B \\ 0.3A=0.2B \\ \frac{0.3A}{0.3}=\frac{0.2B}{0.3} \\ A=\frac{2}{3}B \end{gathered}[/tex]Then, replacing A by (2/3)B on the first equation, we get:
[tex]\begin{gathered} A+B=120 \\ \frac{2}{3}B+B=120 \\ \frac{5}{3}B=120 \\ 3\cdot\frac{5}{3}B=3\cdot120 \\ 5B=360 \\ \frac{5B}{5}=\frac{360}{5} \\ B=72 \end{gathered}[/tex]Finally, A is equal to:
[tex]\begin{gathered} A=\frac{2}{3}B \\ A=\frac{2}{3}(72) \\ A=48 \end{gathered}[/tex]Therefore, she should use 48o
Let[
In a board game, a certain number of points is awarded to a player upon rolling a sixsided die (labeled 1 to 6) according to the function f(x) = 4x +3, where x is thevalue rolled on the die. Find and interpret the given function values and determine anappropriate domain for the function.
ANSWER:
11, 2, 11, makes sense
25, 5.5, 25, does not makes sense
31, 7, 31, does not makes sense
Intergers in a <= x <= b
a = 1 and b = 6
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=4x+3[/tex]where x is the value rolled on the die
The die can land on the numbers 1, 2, 3, 4, 5 and 6.
Therefore:
when x is 2:
[tex]\begin{gathered} f(2)=4\cdot2+3=8+3=11 \\ f(2)=11 \end{gathered}[/tex]f(2) = 11, meaning when a 2 is rolled on the die, the player is awarded 11 points. This interpretation makes sense in the context problem.
when x is 5.5:
[tex]\begin{gathered} f(5.5)=4\cdot5.5+3=22+3=25 \\ f(5.5)=25 \end{gathered}[/tex]f(5.5) = 25, meaning when a 5.5 is rolled on the die, the player is awarded 25 points. This interpretation does not makes sense in the context problem.
when x is 7:
[tex]\begin{gathered} f(7)=4\cdot7+3=28+3=31 \\ f(7)=31 \end{gathered}[/tex]f(7) = 31, meaning when a 7 is rolled on the die, the player is awarded 31 points. This interpretation does not makes sense in the context problem.
Based on the observations above, it is clear that an appropiate domain for the funcion is intergers in a <= x <= b
a = 1 and b = 6
How do I do this? What do I do with the 68 and 79 on each?
hello
solve the first problem, we are to find the missing angle
to solve for x, i had to make up new characters to find missing sides
first of all, let's solve for y
[tex]\begin{gathered} 45+y=180 \\ \text{reason:angle on a straight line is equal to 180 degr}e \\ y=180-45=135^0 \end{gathered}[/tex]let's use this knowledge to solve for z
[tex]\begin{gathered} y+z=180 \\ \text{reason: angles on a straight line = 180} \\ 135+z=180 \\ z=45^0 \end{gathered}[/tex]note: z= 45, we can as well use opposite angles are equal theorem
we should solve for angle a now
[tex]\begin{gathered} 60+z+a=180^0 \\ \text{reason:sum of angles in a triangle is equal to 180 degre}es \\ 60+45+a=180 \\ 105+a=180 \\ a=180-105 \\ a=75^0 \end{gathered}[/tex]we ca use the knowledge of a to solve for b
[tex]\begin{gathered} a+68+b=180^0 \\ \text{reason:angles on a straight line is equal to 180 degr}ees \\ 75+68+b=180_{} \\ 143+b=180 \\ b=180-143 \\ b=37^0 \end{gathered}[/tex]let's use the value of b to solve for c
[tex]\begin{gathered} b+100+c=180^0 \\ \text{reason:sum of angles in a triangle is equal to 180 degre}e \\ 37+100+c=180 \\ 137+c=180 \\ c=180-137 \\ c=43^0 \end{gathered}[/tex]finally, we can solve for x
[tex]\begin{gathered} c+x=180^0 \\ c=43^0 \\ 43+x=180 \\ x=180-43 \\ x=137^0 \end{gathered}[/tex]the value of the unknown angle is equal to 137 degrees
What will the new equation 2 be whenmultiplying everything by-2?
In order to calculate the new equation, we just need to multiply every term in the equation by (-2). So we have that:
[tex]\begin{gathered} (2a+3b=5)\cdot(-2) \\ 2a\cdot(-2)+3b\cdot(-2)=5\cdot(-2) \\ -4a-6b=-10 \end{gathered}[/tex]So the answer is the first option.
can you help me please
When a and b are parallel.
The sum of supplementary angles is180º
m ∠ b + m ∠ a = 180º
(4x-5)+ (13x -2)= 180º
17 x -7 = 180ª
17 x = 180 +7
x= 187/ 17
x = 11
MAT 115 StatisticsWhich of the following probabilities for the sample points A, B, and C could be true if A, B, and C are the only sample points in an experiment?Explain why each of the other 3 answers are wrong.1) P(A) = 5/10, P(B) = 2/10, P(C) = 1/102) P(A) = 0, P(B) = 1/2, P(C) = 1/23) P(A) = 1/5, P(B) = 1/6, P(C) = 1/34) P(A) = -1/10, P(B) = 1/2, P(C) = 6/10
The addition of the 3 probabilities must be equal to 1.
1) P(A) + P(B) + P(C) = 5/10 + 2/10 + 1/10 = 4/5 ≠ 1
2) P(A) + P(B) + P(C) = 0 + 1/2 + 1/2 = 1
3) P(A) + P(B) + P(C) = 1/5+ 1/6 + 1/3 = 7/10 ≠ 1
4) a probability can't be negative
Then, the correct option is option 2
The proportional relationship between the number of sweaters a cothing store buys and sells, s, and the profit, in dollars and cents, that it makes off those sweaters, can be represented by the equation p 238. What is the constant of proportionality from the number of sweaters to the total profit, in dollars and cents?
Proportional relationship formula
[tex]y=kx[/tex]where x and y are the variables, and k is the constant of proportionality.
In this case, the variables are s and p. The equation that relates them is:
[tex]p=23s[/tex]Comparing it with the general formula, the constant of proportionality is:
[tex]k=23[/tex]Simplify the following expression using the change of base formula: log12 7. Round to the nearest hundredth.
Answer:
The expression is given below as
[tex]\log_{12}7[/tex]Let the expression above be equal to x
[tex]\log_{12}7=x[/tex]Concept:
Apply the logarithm change of base formula below
[tex]\begin{gathered} \log_aB=x \\ B=a^x \end{gathered}[/tex]By applying the concept above we will have
[tex]\begin{gathered} \operatorname{\log}_{12}7=x \\ 12^x=7 \\ take\text{ ln of both sides } \\ ln12^x=ln7 \\ xln12=ln7 \\ divide\text{ both sides by ln 12} \\ \frac{xln12}{ln12}=\frac{ln7}{ln12} \\ x=\frac{ln7}{ln12} \\ x=0.7831 \\ x\approx0.78\left(nearest\text{ hundredth\rparen}\right? \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow0.78[/tex]In 3 Years ago Mateo wants to buy a bicycle that costs 700.00. if he opens a savings account that earns 10% interest compounded quarterly how much will he have to despoit as principal to have enough money in 3 years to buy the bike
Answer:
He have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.
[tex]\text{ \$520.49}[/tex]Explanation:
The formula for calculating the Future value of Compound interest is;
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where;
A = Future Value/Amount
P = Principal
r = Interest rate (decimal)
n = number of times the interest is compounded per unit time "t"
t = Time
Making the Principal P the subject of formula;
[tex]P=\frac{A}{(1+\frac{r}{n})^{nt}}[/tex]Given;
A = $700.00
r = 10% = 0.10
n = compounded quarterly (4 times a year) = 4
t = 3 years
substituting the given values;
[tex]\begin{gathered} P=\frac{\text{ \$700.00}}{(1+\frac{0.10}{4})^{4(3)}}=\frac{\text{ \$700.00}}{(1.025)^{12}} \\ P=\text{ \$520.49} \end{gathered}[/tex]Therefore, he have to deposit $520.49 as Principal to have enough money in 3 years to buy the bike.
[tex]\text{ \$520.49}[/tex]2. James went to Target and bought a new tv. He was so excited to find out they had anextra 35% off the already sale price. The TV was $135, but was on sale for $108.99.How much was James' final price with the 35% off discount?Original Cost:Discount:New Price
%35 off the sale price
Original price: $135
Sale: $108.99
Multiply the sale price by the percentage off in decimal form:
108.99 x (35/100) = $38.15 (Discount)
Subtract that amount to the sale price:
108.99-38.15 = $70.84 (final price)
Rotate the yellow dot to a location of pie radians. After you rotate the angle, determinethe value of cos(pie). to the nearest hundredth.-i already figured out the rotation
Okay, here we have this:
Considering the provided angle, we are going to calculate the requested cosine, so we obtain the following:
Then to obtain the cosine we will review the following image of the unit triangle:
So since pi radians is equal to 180°, we can see in the image that the cosine of 180 degrees is equal to -1, so we finally get that the cosine of the angle is -1.
Emily is making a quilt and she has determined she needs 523 square inches of gray fabric and 1318 square inches of burgundy. How many square yards of each material will she need? Round your answers up to the nearest quarter yard. a.) The gray fabric: b.) The burgundy fabric: c.) How many total yards of fabric will she have to buy?
Before we can determine what are being asked, let's first identify the equivalent of an inch to a yard. We get,
[tex]\text{ 1 yard = }36\text{ inches}[/tex][tex]\text{ 1 square yard}^{}=1296\text{ square inches}[/tex]Since we are asked to answer in yards, let's convert the given measures of Gray Fabric and Burgundy.
[tex]\text{Gray Fabric = 523 (in}^2)\text{ x }\frac{1\text{ y}d^2}{1296(in^2)}\text{ = }\frac{523}{1296}=0.40yd^2^{}[/tex][tex]\text{ Burgundy Fabric = 1318 (in}^2)\text{ x }\frac{1yd^2}{1296(in^2)}\text{ = }\frac{1318}{1296}=1.02yd^2[/tex]a.) Gray Fabric = 523 in.^2 = 0.40 yd.^2
b.) Burgundy Fabric = 1318 in.^2 = 1.02 yd.^2
c.) Total yards of fabric Emily will buy = 0.40 yd.^2 + 1.02 yd.^2 = 1.42 yd.^2
Find c for the inequality two thirds times c plus 7 is less than or equal to one third
A c ≤ −6
B c ≥ −6
C c ≤ −10
D c ≥ −10
The inequality has its solution to be option (c) c ≤ -10
How to solve the inequality?From the question, the inequality expression is given as
two thirds times c plus 7 is less than or equal to one third
Rewrite properly as
2/3c + 7 ≤ 1/3
To start with, we subtract 7 from all sides of the inequality
This is represented as
2/3c + 7 - 7 ≤ 1/3 - 7
Evaluate the difference
So, we have
2/3c ≤ -20/3
Multiply through by 3
2c ≤ -20
Divide through by 2
c ≤ -10
Hence, the solution to the inequality is c ≤ -10
Read more about inequality at
https://brainly.com/question/25275758
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match the steps to find the equation of the parabola with Focus (-1, 2), and directrix x=5,find the distance from the focus to the point on the parabola write te equation of the parabolachoose a point on the parabola square both sides and simplifyset the distance from the focus to the point equal to the distance from directrix to the point find the distance from the point on the parabola to the directrix
1. Choose a point on the parabola
[tex](x,y)[/tex]2. Find the distance from the focus to the point on the parabola.
[tex]\sqrt[]{(x+1)^2+(y-2)^2}[/tex]3. Find the distance from the point on the parabola to the directrix.
[tex]\sqrt[]{(x-5)^2}[/tex]4. Set the distance from the focus to the point equal to the distance from directrix to the point.
[tex]\sqrt[]{(x+1)^2+(y-2)^2}=\sqrt[]{(x-5)^2}[/tex]5. Square both sides and simplify
[tex]\begin{gathered} (x+1)^2+(y-2)^2=(x-5)^2 \\ \end{gathered}[/tex]6. Write the equation of the parabola.
[tex]x=-\frac{y^2}{12}+\frac{y}{3}+\frac{5}{3}_{}[/tex]Find the area under the standard normal curve to the left of z=-0.89 and to the right of z= 2.56Round your answer to four decimal places of necessary
We want to find
P(z < - 0.89 U z > 2.56)
= P(z < - 0.89) + P(z > 2.56)
P(z > 2.56) = 1 - P(z ≤ 2.56)
From the normal distribution table, the area to the left of z = - 0.89 = 0.1867
Thus,
P(z < - 0.89) = 0.1867
From the normal distribution table, the area to the left of z = 2.56 = 0.9948
P(z > 2.56) = 1 - 0.9948 = 0.0052
Thus,
P(z < - 0.89 U z > 2.56) = 0.1867 + 0.0052
P(z < - 0.89 U z > 2.56) = 0.1919
The area is 0.1919
In the diagram, es and PR bisect each other at point T. Find the measure of
Since QS and PR bisect each other at point T, triangles QTP and RTS are similar. Hence, we ca draw the following picture:
and we can see that x+48 must be equal to 2x:
[tex]2x=x+48[/tex]and we can solve this equation for the unknow x as
[tex]\begin{gathered} 2x-x=48 \\ x=48 \end{gathered}[/tex]Now, with the value x, the angle P is equal to
[tex]\begin{gathered} P=48+48 \\ P=96 \end{gathered}[/tex]and the answer is a.