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3 years ago

GCF OF 14 AND 28 please explain

Mathematics

2 answers:

KatRina [158]3 years ago

8 0

Answer:

Step-by-step explanation:

both of them can be divided by 14 and thats the greatest number that they both have in common

Molodets [167]3 years ago

4 0

Answer: 7

Step-by-step explanation:

Because 7 and 28 both have the factors of 7 which is the largest common factor

( 7 x 2 ) ( 7 x 4 )

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Sarah is carrying out a series of experiments which involve using mcreasing amounts of a chemical. In the

Marianna [84]

Sarah is carrying out a series of experiments which involve using increasing amounts of a chemical. In the first experiment she uses 6g of the chemical and in the second experiment she uses 7.8 g of the chemical

(i)Given that the amounts of the chemical used form an arithmetic progression find the total amount of chemical used in the first 30 experiments

(ii)Instead it is given that the amounts of the chemical used for a geometric progression. Sarah has a total of 1800 g of the chemical available. Show that the greatest number of experiments possible satisfies the inequality: $1.3^N \leq 91$ and use logarithms to calculate the value of N.

Answer:

(a)963 grams

(b)N=17

Step-by-step explanation:

(a)

In the first experiment, Sarah uses 6g of the chemical

In the second experiment, Sarah uses 7.8g of the chemical

If this forms an arithmetic progression:

First term, a =6g

Common difference. d= 7.8 -6 =1.8 g

Therefore:

Total Amount of chemical used in the first 30 experiments

$S_n=\dfrac{n}{2}[2a+(n-1)d] \\S_{30}=\dfrac{30}{2}[2*6+(30-1)1.8] \\=15[12+29*1.8]\\=15[12+52.2]\\=15*64.2\\=963$ grams$

Sarah uses 963 grams in the first 30 experiments.

(b) If the increase is geometric

First Term, a=6g

Common ratio, r =7.8/6 =1.3

Sarah has a total of 1800 g

Therefore:

Sum of a geometric sequence

$S_n=\dfrac{a(r^N-1)}{r-1} \\1800=\dfrac{6(1.3^N-1)}{1.3-1} \\1800=\dfrac{6(1.3^N-1)}{0.3}\\$Cross multiply\\1800*0.3=6(1.3^N-1)\\6(1.3^N-1)=540\\1.3^N-1=540\div 6\\1.3^N-1=90\\1.3^N=90+1\\1.3^N=91$

Therefore, the greatest possible number of experiments satisfies the inequality

$1.3^N \leq 91$

Next, we solve for N

Changing $1.3^N \leq 91$ to logarithm form, we obtain:

$N \leq log_{1.3}91\\N \leq \dfrac{log 91}{log 1.3}\\ N \leq 17.19$

Therefore, the number of possible experiments, N=17

3 0

3 years ago

At the beginning of the school year, Rochelle joins the school garden club. In her plot of land, she plants 4 rows of tulips, ea

igor_vitrenko [27]

4 rows times 27 bulbs = 108

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3 years ago

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A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 439.0 gram setting.

Vlada [557]

<h2>Answer with explanation:</h2>

Let $\mu$ be the average weight of chocolate chips in each bag.

As per given , we have

$H_0: \mu =439.0\\\\ H_a: \mu$

Since $H_a$ is left-tailed , so we perform a left-tailed test.

Also, the population standard deviation is known $\sigm=21.0$ .

So we use z-test.

Test statistic : $z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqt{n}}}$

Substitute given value , $\overline{x}=433.0\ , n=47,\ \sigma=21 \ , \mu=439$

$z=\dfrac{433-439}{\dfrac{21}{\sqrt{47}}}\approx-1.96$

Significance level = 0.05

Decision rule : Reject $H_0$ when p-value < 0.05.

By z-table , P- value for left-tailed test = P(z<-1.96)= 1- P(z<1.96)

[∵ P(Z<-z)=1-P(Z<z)]

= 1- 0.9750

=0.025

Since , P-value(0.025) < 0.05 , so we reject the null hypothesis.

We support the claim that the machine is underfilling the bags at 0.05 significance level .

3 0

3 years ago

Please show work and if possible explain how you did it? I've been confused over this (both questions please)

Ahat [919]

Y=mx+b
m=slope
b=y intercept or where the line crosses the y axis

slope=rise/run, from left to right

so

1.
ok, so we see it is going throught (-2,1) and (-1,4)
so it hits (-2,1) and then goes up 3 and right 1
so sloe=3/1 or 3
y intercept, it hits at y=7 so
y=3x+7 is equation

2.
we gots a hit at (0,2) and (5,6) about
so goes up 4 and to the right 3 so
4/3 is slope
hits y axis at about y=2
y=(4/3)x+2

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4 years ago

The value of <br> √<br> 40<br> falls between which two numbers?

Aleonysh [2.5K]

Answer:√40 to be the square root of 40, and can investigate between which two whole numbers it lies. The number 40 lies between 36 and 49 hence √40 lies between 6 and 7.

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3 years ago

Read 2 more answers