1. Variable
• x: number of passengers
From the description of the problem, the number of passengers must be at most 3000. Mathematically:
x ≤ 3000
This inequality can be represented in a number line as follows:
Define an exponential function, h(x), which passes through the points (1,16) and(5, 1296). Enter your answer in the form a*b^xh(x) =
We want the answer in exponential form:
[tex]h(x)=a\cdot b^x[/tex]where a and b are the constants to be determined. We can find a and b by substituting the given points and construct a system of equatons, that is, by replacing point (1,16) we have
[tex]\begin{gathered} 16=a\cdot b^1 \\ so \\ 16=a\cdot b \end{gathered}[/tex]and by substituting point (5,1296), we get
[tex]1296=a\cdot b^5[/tex]Then, we have 2 equations in 2 unknonws:
[tex]\begin{gathered} a\mathrm{}b=16 \\ a\mathrm{}b^5=1296 \end{gathered}[/tex]By isolating a from the first equation and substituting this result into the second one, we get
[tex]\begin{gathered} (\frac{16}{b})b^5=1296 \\ \end{gathered}[/tex]which gives
[tex]\begin{gathered} 16b^4=1296 \\ b^4=\frac{1296}{16} \\ b^4=81 \\ b=\sqrt[4]{81} \\ b=3 \end{gathered}[/tex]Then, by substituting this result into the first equation of our system, we obtain
[tex]\begin{gathered} a\cdot3=16 \\ \text{then} \\ a=\frac{16}{3} \end{gathered}[/tex]Therefore, the answer is
[tex]h(x)=\frac{16}{3}\cdot(3)^x[/tex]A pancake recipe for Christ 3 1/3 cups of milk to 1 cup of flour. At 3 3/4 cups of milk is used, what quantity of flour will be needed, according to the recipe?
Given:
3 1/3 cups of milk to 1 cup of flour
3 3/4 cups of milk
So:
[tex]\frac{3\frac{1}{3}}{3\frac{3}{4}}=\frac{1}{x}[/tex]Simplify:
[tex]\begin{gathered} \frac{\frac{10}{3}}{\frac{15}{4}}=\frac{1}{x} \\ \frac{10\times4}{3\times15}=\frac{1}{x} \\ \frac{40}{45}=\frac{1}{x} \\ \frac{8}{9}=\frac{1}{x} \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 8\cdot x=1\cdot9 \\ 8x=9 \\ \frac{8x}{8}=\frac{9}{8} \\ x=\frac{9}{8}=1\frac{1}{8} \end{gathered}[/tex]Answer:
[tex]1\frac{1}{8}[/tex]Slope: -1
Point 3,-5
The Rodriguez family has a fixed incomeof $4,000 a month. Their fixed expensesare $1,800 a month. They save at leastone fourth of the remaining income eachmonth. What is the minimum amountsaved by the Rodriguez family in a year?
we know that
The Rodriguez family has a fixed income of $4,000 a month.
Their fixed expenses are $1,800 a month
so
The remaining amount in a month is
4,000-1,800=$2,200
The one fourth of the remaining income is
(1/4)(2,200)=$550
To find out the minimum amount in a year, multiply $550 by 12
550*(12)=$6,600
therefore
the answer is$6,600If y varies jointly as x and z when x = 5, y = 80, and z = 8. what is y when x = 16 and z = 2?
We are given that y varies jointly as x and z
Mathematically,
[tex]y=kxz[/tex]Where k is the constant of proportionality.
When x = 5, y = 80, and z = 8
[tex]\begin{gathered} y=kxz \\ 80=k\cdot5\cdot8 \\ k=\frac{80}{5\cdot8} \\ k=2 \end{gathered}[/tex]So, the relationship becomes
[tex]y=2xz[/tex]What is y when x = 16 and z = 2?
[tex]\begin{gathered} y=2xz \\ y=2\cdot16\cdot2 \\ y=64 \end{gathered}[/tex]Therefore, the value of y is 64
Which expressions are equal to 10^5? ☐ (10^4)¹ 10³x10² 1/10^5 (10³) ² 10x10x10x10x10
Using the rule of exponents, the only expressions that are equal to 10⁵ are; 10³x10² and 10x10x10x10x10
How to use Laws of Exponents?
The laws of exponents are as follows;
1) The Product Rule for Exponents: To get the product of two numbers that have the same base, ensure you add the exponents.
2) The Quotient Rule for Exponents: To get the quotient of two numbers that have the same base, ensure that you subtract the exponent of the denominator from the exponent of the numerator.
3) The Power Rule for Exponents: To raise a number with an exponent to a power, ensure that you multiply the exponent times the power.
4) Negative Exponent Rule: Make sure to Invert the base in order to change a negative exponent into a positive.
5) Any non-zero number that is raised to the zeroth power is 1.
We want to find an expression that is equivalent to 10⁵. Thus, applying the rules of exponents above, the only one that is correct is 10 ³x 10² or 10x10x10x10x10
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At an aquarium, researchers are preparing a mixture of salt water. The desired ratio is 90 grams of salt per liter of water.1 ounce= 28.35 grams1 gallon= 3.8 literswhat is the ratio in ounces per gallon
Based on the question, the ratio of the salt mixture is:
[tex]\frac{90grams}{1\text{liter}}[/tex]So, if we have 3.8 liters in 1 gallon, we would need 90grams x 3.8 = 342 grams of salt in 1 gallon.
[tex]\frac{90grams}{1\text{liter}}\times\frac{3.8liters}{1\text{gal}}=\frac{342grams\text{ }}{1gal}[/tex]The next step is to determine how many ounces are there in 342 grams. If 1 ounce = 28.35 grams, then 342 grams divide 28.35 grams = 12.06. Hence, in 342 grams, there are 12.06 ounces.
Thus, we can say that:
[tex]\frac{342\text{grams}}{1\text{gal}}=\frac{12.06\text{ounces}}{1\text{gal}}[/tex]The ratio of the salt mixture is 12.06 ounces per gallon.
subtract P - 2 q + r from the sum of 10 P - R and 5 p + q
Answer:
14p +4q-2r
Step-by-step explanation:
Sum of (10p-r+5p+2q)
10p+5p+2q-r
15p+2q-r
Now subtract( p-2q+r) from (15p+2q-r)
(15p+2q-r) - (p-2q+r)
15p+2q-r-p+2q-r
15p-p+2q+2q-r-r
14p +4q-2r
The answer is 14p +4q-2r
Find the greatest common factor for the list of monomials. 20x4y2z, 4x4y, 60x3y3 The greatest common factor is
The monomials given are:
[tex]\begin{gathered} 20x^4y^2z \\ 4x^4y \\ 60x^3y^3 \end{gathered}[/tex]First, we will write each monomial as a product of each individual factors. So,
[tex]\begin{gathered} 20x^4y^2z=2\cdot2\cdot5\cdot x\cdot x\cdot x\cdot x\cdot y\cdot y\cdot z \\ 4x^4y=2\cdot2\cdot x\cdot x\cdot x\cdot x\cdot y \\ 60x^3y^3=2\cdot2\cdot3\cdot5\cdot x\cdot x\cdot x\cdot y\cdot y\cdot y \end{gathered}[/tex]Now, we will circle the factors/numbers that are common to all 3 monomials.
That is,
Thus, we can write the GCF as,
[tex]\begin{gathered} 2\cdot2\cdot x\cdot x\cdot x\cdot y \\ =4x^3y \end{gathered}[/tex]You spin a spinner with 5 sections: 1 yellow (Y), 1 purple (P), 1red (R), 1 blue (B), and 1 green (G).What is the sample space for one spin of this spinner?
Given:
The spinner has five sections that are 1 yellow (Y), 1 purple (P), 1 red (R), 1 blue (B), and 1 green (G).
Required:
We need to find the sample space for one spin of the given spinner.
Explanation:
The sample space = the collection of all sections of the spinner.
[tex]S=\lbrace\text{ yellow, purple, red, blue, green \textbraceright}[/tex][tex]S=\lbrace\text{ Y, P, R, B, G\textbraceright}[/tex]Final answer:
[tex]\lbrace\text{ Y, P, R, B, G\textbraceright}[/tex]Option D is correct.
Mike read of a novel. Katy read as much of the same novel as Mike. How much of the novel did Katy read?
What type of comparison is shown in the question above?
A.
additive comparison
B.
multiplicative comparison
The type of comparison shown is multiplicative comparison.
As the number of novel increase in the case of Mike, the number for Katy will also increase simultaneously.
For example, if the novel read count for Mike is 3 then the novel read count for Katy will be also 3.
Additive comparison defines a relationship between two quantities by specifying or saying how much greater or less one is than the other.
Multiplicative Compare - compares two values and multiplies one by a specified number to get the other.
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help me please
thank you
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex](-\infty, 4][/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
how do you solve 3/4 % of 387?
To calculate the 3/4% of 387, you have to use cross multiplication:
The fraction 3/4 can be expressed as a decimal value to make the calculations easier: 3/4=0.75
100% is 387
0.75% is x
Both relations are at the same ratio, so that
[tex]\begin{gathered} \frac{387}{100}=\frac{x}{0.75} \\ x=\frac{387}{100}\cdot0.75 \\ x=2.9025 \end{gathered}[/tex]This means that the 3/4% of 387 is 2.9025
1/11 as an decimal for long division
Question: 1/11 as an decimal for long division??
Answer: 1/11 as a decimal is 0.090909090909091.
Step-by-step explanation:
÷= 1
÷=.
(×)÷= .
1÷11=0.0
(×)÷= ,,,
1÷11=0.09 , 1 . ÷=.…
÷=.
: )✨
For a standard normal distribution, given:
P(z < c) = 0.9663
Find c.
The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
What is standard normal distribution?
The standard normal distribution table gives the probability of a regularly distributed random variable Z, whose mean is equivalent to 0 and difference equal to 1, is not exactly or equal to z. The normal distribution is a persistent probability distribution.
What is z score?
Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by
z = (x - μ)/σ
Where x is the raw score, μ is the mean and σ is the standard deviation.
Given that P(z < c) = 0. 9663; hence:
From the normal distribution table, c = 0.47
The value of c for a standard normal distribution, P(z < c) = 0. 9663 is 0.47.
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6. Mishell bought some sugar and strawberries to make strawberry jam.Sugar costs $1.80 per pound, and strawberries cost $2.50 per pound.Mishell spent a total of $19.40. Which point on the coordinate plane couldrepresent the pounds of sugar and strawberries that Mishell used to makejam?*
Okay, here we have this:
We obtain the following equation.
Let's take x as pounds of sugar, and y as pound of strawberries:
x(Sugar Costs)+y(Strawberries cost)=Total Cost
x(1.80)+y(2.50)=19.40
We are going to replace the coordinates of each point to see which one satisfies the total cost:
Point A (0,0):
x(1.80)+y(2.50)=19.40
0(1.80)+0(2.50)=19.40
0+0=19.40
0=19.40 (We can see that this equality is false, therefore the option is incorrect)
Point B (8,2):
x(1.80)+y(2.50)=19.40
8(1.80)+2(2.50)=19.40
14.4+5=19.40
19.40=19.40 (This equality is true, therefore this option may be correct, however let's analyze the rest)
Point C (6,1)
x(1.80)+y(2.50)=19.40
6(1.80)+1(2.50)=19.40
10.8+2.5=19.4
13.3=19.4 (We can see that this equality is false, therefore the option is incorrect)
Point D (7, 5)
x(1.80)+y(2.50)=19.40
7(1.80)+5(2.50)=19.40
12.6+12.5=19.40
25.1=19.4 (We can see that this equality is false, therefore the option is incorrect)
Finally we obtain that the correct answer is the Point B.
Mai works a total of 31 hours per week at two jobs. The number of hours she works at a coffee stand is 5 less than 2 times the number of hours she works at the animal shelter. How many hours does Mai work at the animal shelter?
Show the equation you use and your work solving the equation.
Answer:
12
Step-by-step explanation:
Let x = number of hours at the shelter
"The number of hours she works at a coffee stand is 5 less than 2 times the number of hours she works at the animal shelter."
The number of hours at the coffee stand is
2x - 5
The total number of hours is 31, so x added to 2x - 5 must equal 31.
2x - 5 + x = 31
3x - 5 = 31
3x = 36
x = 12
She works 12 hours at the shelter.
Solve the following equation using the zero product property 5(-v-5)(v-8)=0
The expression to be solved is:
[tex]5\cdot(-v-5)\cdot3\cdot(v-8)\text{ = 0}[/tex]The zero product property states that the solution to this equation is the values of each term equals to 0.
[tex]\begin{gathered} (-v\text{ - 5) = 0} \\ -v\text{ = 5} \\ v\text{ = -5} \end{gathered}[/tex][tex]\begin{gathered} (v\text{ - 8) = 0} \\ v\text{ = 8} \end{gathered}[/tex]The answers are -5 and 8.
the radius of a circle in 6 miles. what is the area of a sector bounded by a 126° arc?
The area of a sector of a circle is:
[tex]A=\pi r^2\cdot\frac{\theta}{360}[/tex]Where θ is the angle of the arc and r is the radius.
In this case,
• r = 6mi
,• θ = 126º
Then:
[tex]A=\pi(6mi)^2\cdot\frac{126}{360}=\pi\cdot\frac{36mi^2\cdot126}{360}=\frac{63}{5}\pi[/tex]Thus the correct option is the 4th one:
[tex]\frac{63}{5}\pi\text{ }mi^2[/tex]g+3 1/2=10 answer to g
Answer:
Exact form: G = 12/2
decimal form: G = 6.5
4. The table represents a proportional relationship. Find the constant ofproportionality and write an equation to represent the relationship.aу23110103124Constant of proportionality:Equation: y =
Given the table which represents a proportional relationship
The general form for a proportional relationship is :
[tex]y=k\cdot a[/tex]Where k is the constant of the proportionality
As shown in the table :
when a = 2 , y = 2/3
And when a = 3 , y = 1
It is better to substitute with the second row
[tex]\begin{gathered} a=3\rightarrow y=1 \\ \\ 1=k\cdot3 \\ \\ k=\frac{1}{3} \end{gathered}[/tex]So, the equation will be :
[tex]y=\frac{1}{3}a[/tex]
Usqqe format HTH to mean that the first toss is heads, the second is tails and the third is heads more than one element in the set, separate them with commas
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: State the number of outcomes possible for three tossing of a coin
Since a coin has two possible outcomes and is tossed three times, the total outcomes will be:
[tex]\begin{gathered} 2^3=8 \\ 8\text{ outcomes} \end{gathered}[/tex]STEP 2: Find the number of sample spaces for the three tosses
STEP 3: Get the outcomes of the events for which the second toss is tails
Hence, the answers are given as:
Sample Space:
[tex]\lbrace HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\rbrace[/tex]The event that the second toss is tails:
[tex]\lbrace HTH,HTT,TTH,TTT\rbrace[/tex]30 cars are in a race. In how many different ways can cars finish in the top 3 positions?
Given:
There are 30 cars in a race.
The number of ways that cars finish in the top 3 positions is given as,
[tex]\begin{gathered} ^nP_r=\frac{n!}{(n-r)!} \\ n=30,r=3 \\ ^{30}P_3=\frac{30!}{(30-3)!} \\ =\frac{30!}{27!} \\ =28\times29\times30 \\ =24360 \end{gathered}[/tex]Answer: There are 24360 ways that cars finish in the top 3 positions.
If sin 0
=
40/41 and lies in Quadrant I, what does tan theta equal to?
answer of this trigonometric function is 4.49
what is trigonometric function?
The trigonometric functions are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths. They are also known as circular functions, angle functions, or goniometric functions.
LETS ASSUME Given sinθ= 40/41
tan(θ)= sinθ/[tex]\sqrt{1-sin^{2} (theta) }[/tex]....(1)
putting sin theta value in (1)
⇒tan(θ)= 4.49
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Find loss and loss percent.
cost price = 850
selling price = €595
3.5.3 Test (CST): Functions Does this graph show a function? Explain how you know. 66 PE -2 E C N 6 8 A. No; there are y-values that have more than one x-value. B. Yes; the graph passes the vertical line test. C. Yes; there are no y-values that have more than one x-value. D. No; the graph fails the vertical line test. here is the answer for the people who need it
Write the following decimal number in standard form Two and four hundredths
ANSWER
[tex]The\text{ standard form of 2.04 is 2.04}\times10^0[/tex]STEP-BY-STEP EXPLANATION
We are two convert decimal numbers to standard form
Given information
Two and four hundredths
Step 1; write the above data in decimal
[tex]\begin{gathered} \text{four hundredths } \\ 4\text{ x }\frac{1}{100} \\ \frac{4}{100\text{ }}\text{ = 0.04} \end{gathered}[/tex]Step 2: Add the four hundredths to two
[tex]\text{ 2 + 0.04 = }2.04[/tex]Step 3: convert the decimal to standard form
[tex]2.04\text{ }\times10^0[/tex]Which expression simplifies to 5? 7 points A. 27/3 -- 14 B. 27/3 + 4 C. --27/3 -- 4 D. --27/3 + 4
The expression simplifies to 5 is -27/3 +14 .
The option D is correct.
What is Simplification?
Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.
Given,
Which expression simplifies to 5?
Here, Options are
A. 27/3 - 14
= 9 - 14 = -5
B. 27/3 + 4
= 9 + 4 = 13
C. --27/3 - 4
= -9 - 4 = -13
D. -27/3 +14
= -9 + 14 = 5
Hence, The expression simplifies to 5 is -27/3 +14 .
The option D is correct.
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Please help and provide explanation I want to understand this!
We will have to find the equation that follows the form:
[tex]a+bx=y[/tex]That is:
*The value of a is:
[tex]a=547.4666667[/tex]*The value of b is:
[tex]b=29.91428571[/tex]So, the linear regression is:
[tex]y=29.91428571x+547.4666667[/tex]We can see it graphically as follows:
Here we can see the linear regression line and the points used.
***How to manually determine linear regressions***
We will start as follows:
We will have to use the following expressions in order to manually find the linear regression:
[tex]b=\frac{n(\sum^{}_{}xy)-(\sum^{}_{}x)(\sum^{}_{}y)}{n(\sum^{}_{}x^2)-(\sum^{}_{}x)^2}[/tex]And:
[tex]a=\frac{\sum ^{}_{}y-b(\sum ^{}_{}x)}{n}[/tex]Here we have that n is the number of values on the dataset. So, we solve for b as follows [Based on the problem given]:
*We will determine the values of n, the sum of x, the sum of y, xy, x^2 & y^2 as follows:
Sum of x:
[tex]\sum ^{}_{}x=1+2+3+4+5+6\Rightarrow\sum ^{}_{}x=21[/tex]Sum of y:
[tex]\sum ^{}_{}y=588+298+640+650+707+730\Rightarrow\sum ^{}_{}y=3913[/tex]Value of n: We have that the number of datasets given is 6 [6 pairs of values on the table].
[tex]n=6[/tex]*The sum of xy:
[tex]\sum ^{}_{}xy=(1)(588)+(2)(598)+(3)(640)+(4)(650)+(5)(707)+(6)(730)\Rightarrow\sum ^{}_{}xy=14219[/tex]*The sum of X^2:
[tex]\sum ^{}_{}x^2=1^2+2^2+3^2+4^2+5^2+6^2\Rightarrow\sum ^{}_{}x^2=91[/tex]*The square of the sum of x:
[tex](\sum ^{}_{}x)^2=21^2\Rightarrow(\sum ^{}_{}x)^2=441[/tex]Now that we have all the values, we replace in the first equation and solve for b:
[tex]b=\frac{(6)(14219)-(21)(3913)}{(6)(91)-(441)}\Rightarrow b=29.91428571[/tex]And we solve now for a:
[tex]a=\frac{(3913)-(29.91428571)(21)}{(6)}\Rightarrow a=548.4666667[/tex]And then we simply replace on the expression:
[tex]y=bx+a[/tex]And the expression after the replacement of a & b is the linear regression.
First Drop down: Yes or NOSend drop down: is or is not
Looking at the number line, the length between 0 and 1 is not divided into 3 equal parts. Hence, the answer is no. Victoria is not correct.
First drop-down: No
Second drop-down: is not
