First, we have "at least 120 bagels"
So we write ≥120 bagels.
Now, we are given that:-
Mrs. Trevino already has 2 dozen bagels.
Remember, a dozen is equal to 12, so if we have 2 dozen, then we have
[tex]\sf{2*12=24}\longleftarrow\sf{Mrs.Trevino~already~has~24~bagels}[/tex]
Now, she'll buy the remaining bagels in packages of 6, so we write
6x (packages of 6)
So the inequality looks like so:-
[tex]\sf{6x+24\geq 120}[/tex]
Now, let's solve the inequality :)
First, subtract 24 from both sides:-
[tex]\sf{6x\geq 120-24}[/tex]
[tex]\sf{6x\geq 96}[/tex]
Divide both sides by 6:-
[tex]\bigstar{\boxed{\pmb{x\geq 16}}}\longleftarrow\sf{number~of~packages~she~should~buy}[/tex]
note:-Hope everything is clear :)
Find the volume of the figure below.
Answer:
C) 2808
Step-by-step explanation:
Volume of Triangular Prism = 1/2 x height x length x base
= 1/2 * 9 * 24 * 26
= 2808 mm^3
I hope my answer helps you.
if a town with a population of 10,000 doubles in size every 17years wat will population be 68 years from now
Answer:
20,000×17 gives 340,000
340,000×68 which gives 23,120,000
Solve the quadratic equation by using a numeric approach.
0.02x squared + 0.1 x - 2 = 0
a.
x = 2.3 and x = -29.2
c.
x = 5.6 and x = -12.2
b.
x = 7.8 and x = -12.8
d.
x = 1.3 and x = -22.6
Answer:
The option b) is correct (x = 7.8 and x = -12.8)
For the verification picture is below
I hope my answer helps you.
Chart Rodrigo's total utility for lattes and the marginal utility for the same using information
from the table.
Quantity
Utility
0
14
2
3
4
on ANO
22
28
32
35
5
1)
40
30
Units of Total Utility
20
10
0
1
2
3
4
N
5
Number of Lattés
2)
)
20
15
Units of Total Utility per Latte
10
5
0
1
2
3
4 5
Number of Lattés
The marginal utility is the extra satisfaction derived from the consumption of a product.
How to illustrate the marginal utility?Your information isn't well written. Therefore, an overview of utility will be given. The total utility is the total amount of satisfaction that a consumer derives from a product.
The marginal utility simply means the extra satisfaction that's gotten from a product when an additional unit is consumed.
The formula for marginal utility will be:
= Total utility difference/Quantity of goods difference
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what is the inverse of f(x)=x^2+5
Answer:
[tex]\sqrt{X-5}[/tex], [tex]-\sqrt{X-5}[/tex]
Step-by-step explanation:
Replace X with Y
solve for Y; X = Y^2 + 5
subtract 5 from both sides
X - 5 = Y^2
take the square root
Y = plus or minus sqrt(X-5)
sqrt(X-5); -sqrt(X-5)
The cubic root of 400 lies between which two numbers?
Answer:
Let x = cube root of 400
Using a calculator x = 7.368 to 3 decimal places
So: 7 < x < 8
Find the area of the shaded polygon
Answer:
372
Step-by-step explanation:
area of trapezium = a+b/2 * h
a is the length on top
b is the length on the bottom
h is the height
7+24/2*24=
=372
A washer and dryer cost a total of $1184. The cost of the washer is three times the cost of the dryer. Find the cost of each of them.
The cost of a washer is $1184 while the cost of a drier is $296
Word ProblemGiven Data
Total cost of washer and dryer = $1184let the cost of a washer be = wlet the cost of a drier be = dHence,
w+d = 1184 -------------1
we know that the cost of the washer is three times the cost of the dryer.
w = 3d -------------------2
put w = 3d in equation 1
3d + d = 1184
4d = 1184
d = 1184/4
d = 296
The cost of a drier is $296
put d = $296 in equation 2
w = 3*296
w = $888
Check:
$888+$296 = $1184
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3) You need to paint shutters on a window that is on the second floor of your house. You have a 20 foot ladder that you will use. There is a warning on the ladder that states the angle formed by the ladder and the ground must not be less than 70 degrees, or the ladder may slip and cause serious injury or death. You planned on placing the bottom of the ladder 3 feet from the base of the house. Will the angle formed between the ground and the ladder be safe? What is the furthest possible distance the ladder can be placed to maintain a safe angle? Sketch:
Answer:
See below ↓↓
Step-by-step explanation:
Height of ladder = 20 feetDistance of base of ladder from house = 3 feetAngle must not be < 70°Taking the cos ratio of the angle
Let the angle formed be α cos α = adjacent side / hypotenusecos α = 3 / 20 = 0.15α = cos⁻¹ (0.15)α = 81.37°⇒ The angle formed is safe
Finding furthest possible distance
Take α to be 70°cos 70° = 0.34 = x/20⇒ x = 20 x 0.34 = 6.8 feetAnswer:
Yes, the angle formed between the ground and the ladder is safe
6.84 ft (nearest hundredth)
Step-by-step explanation:
We can use the cos trig ratio to determine the angle made between the 20ft ladder and 3ft from the base of the house (see first attached image for sketch).
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent to the angleH is the hypotenuseGiven:
A = 3 ftH = 20 ft[tex]\sf \implies \cos(\theta)=\dfrac{3}{20}[/tex]
[tex]\sf \implies \theta=\cos^{-1}\left(\dfrac{3}{20}\right)[/tex]
[tex]\sf \implies \theta=81.37307344..^{\circ}[/tex]
Therefore, as the ladder is forming an 81.37° angle and 81.37...° > 70° the angle formed between the ground and the ladder is safe.
To find the furthest possible distance the ladder can be placed, set [tex]\theta[/tex] to 70° (max safe angle) and the hypotenuse (ladder length) to 20, then solve for A (see second attache image for sketch):
[tex]\sf \implies \cos(70^{\circ})=\dfrac{A}{20}[/tex]
[tex]\sf \implies A=20\cos(70^{\circ})[/tex]
[tex]\sf \implies A=6.840402867...\: \sf ft[/tex]
So the furthest possible distance the ladder can be placed to maintain a safe angle is 6.84 ft (nearest hundredth).
Can someone help with these questions??
Will be helpful
How many solutions does the inequality x>12 have?
Answer:
infinte
Step-by-step explanation:
The answer is anything greater than 12 so it would be infinte
What is the answer I need help please
Answer:
i belive the answer is 73
Step-by-step explanation:
45+62=107
180-107=73
Which is the graph of g(x) = (0.5)x + 3 – 4?
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, negative 4).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 3. It crosses the y-axis at (0, 3).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = negative 4. It crosses the y-axis at (0, 4).
On a coordinate plane, an exponential function decreases in quadrant 2 and has a horizontal asymptote at y = 4. It crosses the y-axis at (0, 12).
Mark this and return
Answer:
the graph will be an exponential function that crosses the y-axis at about (0, -4).
Step-by-step explanation:
Answer:
The answer is the first graph.
Step-by-step explanation:
I just did the quiz
What is the least whole number n such that 84 divides n! ?
Answer:
5 should be the correct answer
help pls
just say what option
Answer:
D .the formation in the graph shows a positive non linear correlation, the weight of the dinosaur trends to increase according to its length.hope this helps you :)The information on the graph shows a positive nonlinear correlation and the weight of the dinosaur tends to increase according to its length.
What is a discrete graph?A discrete graph is also known as a scatter plot that shows the discontinuous and the nonlinear data point on the graph.
From the graph, we can see the increasing weight of the Dinosaur size vertical y-axis and the increasing length of the feet on the horizontal x-axis.
Therefore, we can conclude that the data points show an increasing nonlinear weight on the graph as the length increases.
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The population of a city is given by P(t) = Poe
-0.04t where t is time measured in years and
P0 is the population at time t=0. Assume that Po = 1,000,000.
a. Find the population when t=3.
b. During what year will the population drop below 750,000. (solve an equation, no
guess-and-check)
Answer:
a. 885,920
b. year 8
Step-by-step explanation:
The population at a given time is described by the exponential formula ...
P(t) = P0·e^(-0.04t)
where P0 is given as 1,000,000.
a.We are asked for the value of P(3). This ccan be found by substituting 3 for t in the equation and evaluating the numerical expression.
P(3) = 1,000,000·e^(-0.04·3) = 1,000,000·e^(-0.12)
P(3) ≈ 886,920
The population when t=3 is about 886,920.
__
b.We can put the given numbers in the equation and solve for t.
750,000 = 1,000,000·e^(-0.04t)
0.75 = e^(-0.04t) . . . . . divide by 1,000,000
ln(0.75) = -0.04t . . . . . take the natural log
-ln(0.75)/0.04 = t ≈ 7.192
The population will drop below 750,000 in year 8.
_____
Additional comment
These values can be confirmed by a graphing calculator.
Note that "year 1" is the year between t=0 and t=1. So, "year 8" is the year between t=7 and t=8.
|x+1|+|x-2|=3
can someone give an easy explanation plssss
Answer:
The numbers inside |x| is always positive
Step-by-step explanation:
|x+1| ---> x+1
|x-2| ---> x+2
= 3
i need help with this i don't know how to do it.
Answer:
1935 were supporting the home team
Step-by-step explanation:
Since there are 4,500 people attending the game, we must find 43% of that. Doing this, we need to multiply 43% or .43 by 4,500.
After solving, you should get 1,935. There were 1,935 people supporting the home team.
Question 8 of 10
Suppose a sample consists of the following data values. What is the sample
mean?
6,7,3,9,2,4,5,9,9,3,7,8
O A7
B. 6
C. 5
Answer:
whatever number is repeating the most is the answer.
simplify exponents please! need the answer immediately.
Answer:
[tex]\frac{w^{6} }{9 }[/tex]Step-by-step explanation:
Given
[tex]\frac{3^{-2}*k^{0}*w^{0} }{w^{-6} }[/tex]Remember :
Any term raised to the power 0 is equal to 1Solving
[tex]\frac{3^{-2} }{w^{-6} }[/tex][tex]\frac{w^{6} }{9}[/tex]Answer:
[tex]\huge\boxed{\bf\:\frac{w^{6}}{9}}[/tex]
Step-by-step explanation:
[tex]\frac{ 3 ^ { -2 } \times k ^ { 0 } \times w ^ { 0 } }{ w ^ { -6 } }[/tex]
Any number with 0 as its exponent will be equal to 1. So,
[tex]\frac{3^{-2} \times 1 \times 1}{w^{-6}}\\= \frac{3^{-2}}{w^{6}}[/tex]
Now,
[tex]\frac{3^{-2}}{w^{6}}\\= 3^{-2}w^{6}[/tex]
Then,
[tex]3^{-2}w^{6}\\= \frac{1}{3^{2}}w^{6}\\= \frac{1}{9}w^{6}\\= \boxed{\bf\:\frac{w^{6}}{9}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Which value is the solution of
[tex] \sqrt[3]{3x} + 7 = 4[/tex]
A.-9
B.-1
C.3
D.19
Answer:
A
Step-by-step explanation:
[tex]\sqrt[3]{3x}[/tex] + 7 = 4 ( subtract 7 from both sides )
[tex]\sqrt[3]{3x}[/tex] = - 3 ( cube both sides to clear the radical )
3x = (- 3)³ = - 27 ( divide both sides by 3 )
x = - 9
How many pieces of tape measuring 2/3 meter can be cut from a roll of tape that measures 5 1/3 meters
how many pieces of tape can be cutted.
solution:[tex]5 \frac{1}{3} \div \frac{2}{3} [/tex]
[tex] = (5 + 0) + ( \frac{1}{3} + \frac{2}{3} )[/tex]
[tex] = 5 + \frac{1 + 2}{3} [/tex]
[tex] = 5 + \frac{3}{3} [/tex]
[tex] = 5 + \frac{3 \div 3}{3 \div 3} [/tex]
[tex] = 5 + \frac{1}{1} [/tex]
[tex] = 6[/tex]
therefore, 6 pieces of tape can be cutted.
please help me solve this?
Answer:
there are none (sorry if I got it wrong)
Step-by-step explanation:
also, there is none because there other numbers are really close to the other number
outliers are a number that is really small in the pack of numbers and outliers can also be the number that is really big for example I have the numbers 3 24 28 32 43 and then 100. 3 and 100 are outliers because one number (3) is really small from the other numbers are bigger and one number (100) is really big from the other number but sometimes there are no outliers
f(x)=2x^3-6x+k and the remainder when f(x) is divided by x+1=7 then what is the value of k
Given: f(x)=2x(cube)-6x+x
reaminder of f(x) when (x+1) diveded
to find value of k
solution,
f(x)=2x(cube)-6x+k
f(-1)=7
2(-1)(cube)+6+k=7
4+x=7
k=7
Hence,k=7
The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. suppose intensity is 8000 units at a distance of 2 miles. what will the intensity be at a distance of 11 miles? round your answer to the nearest unit. a. 247 units b. 228 units c. 264 units d. 290 units
Answer:
The ratio of the new distance to the old distance is (11/2) .
The intensity is inversely proportional to the square of the distance,
so the new intensity will be (2/11)² times the old intensity.
Intensity = 8,000 (2/11)² =
32,000 / 121 = 262.463 units
Rounded to the nearest whole unit: 262 units
Step-by-step explanation:
264 units of intensity came from a distance of 11 miles option (c) 264 units is correct.
It is given that the intensity is 8000 units at a distance of 2 miles.
It is required to find the intensity at a distance of 2 miles.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station.
Suppose the Intensity of the signal is I and the distance is d, then:
[tex]\rm I \propto\frac{1}{d^2}[/tex]
Intensity from the station [tex]\rm I_1=8000 \ units[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_1=2 \ miles[/tex]
Intensity from the station [tex]=\rm I_2[/tex]
[tex]\rm I_1[/tex] intensity at distance [tex]\rm d_2=11 \ miles[/tex]
[tex]\rm \frac{I_2}{I_1} = \frac{d_1^2}{d_2^2}[/tex] (From the proportional relation)
[tex]\rm \frac{I_2}{8000} = \frac{2^2}{11^2}[/tex]
[tex]\rm I_2 =8000\times\frac{4}{121} \\\\\rm I_2 = 264.46 \ units[/tex] ≈ 264 units
Thus, the 264 units of intensity came from a distance of 11 miles.
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Aiden invested $43,000 in an account paying an interest rate of 9 1/4 % compounded monthly. Hailey invested $43,000 in an account paying an interest rate of 8 7/8% compounded continuously. To the nearest dollar, how much money would Aiden have in his account when Hailey's money has doubled in value?
first off let's change the mixed fractions to improper fractions, and let's Hailey's account first.
[tex]\stackrel{mixed}{9\frac{1}{4}}\implies \cfrac{9\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{37}{4}} ~\hfill \stackrel{mixed}{8\frac{7}{8}}\implies \cfrac{8\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{71}{8}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &\stackrel{43000(2)}{\$86000}\\ P=\textit{original amount deposited}\dotfill & \$43000\\ r=rate\to \frac{71}{8}\%\to \frac{~~ \frac{71}{8}~~}{100}\dotfill &0.08875\\ t=years \end{cases} \\\\\\ 86000=43000e^{0.08875\cdot t}\implies \cfrac{86000}{43000}=e^{0.08875t}\implies 2=e^{0.08875t}[/tex]
[tex]\ln(2)=\ln(e^{0.08875t})\implies \log_e(2)=\log_e(e^{0.08875t})\implies \ln(2)=0.08875t \\\\\\ \cfrac{\ln(2)}{0.08875}=t\implies 7.81\approx t[/tex]
ok, now we know how long it takes for Hailey's money to double, how much money does Aiden have by then?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$43000\\ r=rate\to \frac{37}{4}\%\to \frac{~~ \frac{37}{4}~~}{100}\dotfill &0.0925\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &\frac{\ln(2)}{0.08875} \end{cases}[/tex]
[tex]A=43000\left(1+\frac{0.0925}{12}\right)^{12\cdot \frac{\ln(2)}{0.08875}}\implies A=43000\left( \frac{4837}{4800} \right)^{\frac{12\ln(2)}{0.08875}}\implies \boxed{A\approx 88311}[/tex]
notice, in Hailey's amount we used the logarithmic value for "t", just to avoid any rounding issues.
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 110I I2 + I + 4 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum? I = thousand foot-candles
Using the vertex of a quadratic equation, it is found that P is at a maximum for l = -0.5 thousand foot-candles.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, the function for P is given by:
[tex]P(l) = \frac{110l}{l^2 + l + 4}[/tex]
The function will be at a maximum when the denominator is at a minimum. The denominator is a quadratic function with coefficients a = 1, b = 1, c = 4, hence:
[tex]l_v = -\frac{b}{2a} = -\frac{1}{2} = -0.5[/tex]
P is at a maximum for l = -0.5 thousand foot-candles.
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Is the equation y=5x+1 a linear equation? Explain.
Answer:
Yes
Step-by-step explanation:
Linear equations are equations in which the highest power of the equation is always 1, they look like a straight line when put on graph and they usually have this form: y = ax + b
y = 5x + 1 is a good example of a linear equation but they may also look like: y = 2x (b = 0) or y = x + 3 (a = 1).
Please help me with this math problem!! Will give brainliest!! :)
Answer:
See below
Step-by-step explanation:
From the graph :
y = -x -inf < x <=0
y = x 0<= x <= 2
y = 3 x > 2
Compute x/y if
x + 1/y = 4 and
y + 1/x = 1/4
Please explain the process on how to solve it- I'll give brainliest!
Let first consider the equations one by one and will be solving one by one ;
[tex]{:\implies \quad \sf x+\dfrac{1}{y}=4}[/tex]
Multiplying both sides by y will lead ;
[tex]{:\implies \quad \sf xy+1=4y}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=4y-1\quad \cdots \cdots(i)}}[/tex]
Now, consider the second equation which is ;
[tex]{:\implies \quad \sf y+\dfrac{1}{x}=\dfrac14}[/tex]
Multiplying both sides by x will yield
[tex]{:\implies \quad \sf xy+1=\dfrac{x}{4}}[/tex]
[tex]{:\implies \quad \sf xy=\dfrac{x}{4}-1}[/tex]
[tex]{:\implies \quad \boxed{\sf xy=\dfrac{x-4}{4}\quad \cdots \cdots(ii)}}[/tex]
As LHS of both equations (i) and (ii) are same, so equating both will yield;
[tex]{:\implies \quad \sf 4y-1=\dfrac{x-4}{4}}[/tex]
Multiplying both sides by 4 will yield
[tex]{:\implies \quad \sf 16y-4=x-4}[/tex]
[tex]{:\implies \quad \sf 16y=x}[/tex]
Dividing both sides by y will yield :
[tex]{:\implies \quad \boxed{\bf{\dfrac{x}{y}=16}}}[/tex]
Hence, the required answer is 16